4th International PhD School in Formal Languages and Applications
2005
1st TERM
PROGRAMMES
LANGUAGES
Zoltán Ésik, Rovira i Virgili University, Tarragona
zoltan.esik@urv.net
1. Types of languages (languages of finite and infinite words, finite and
infinite trees, graphs, pictures, etc.) and types of representation.
Formal languages in mathematics and computer science
2. Families of languages. Operations on languages (general operations
on sets, specific operations). Closure of families of languages under
operations. Abstract families of languages. Characterizations and
representations of families of languages
3. Decidability problems on languages. Descriptional complexity
measures for languages. Languages and computational complexity
References
Hopcroft, J.E., R. Motwani & J.D. Ullman (2000), Introduction to Automata
Theory, Languages, and Computation, 3rd ed. Addison-Wesley, Reading, MA.
Papadimitriou, C. (1994), Computational Complexity. Addison-Wesley,
Reading, MA.
Rozenberg, G. & A. Salomaa, eds. (1997), Handbook of Formal Languages,
3 vols. Springer, Berlin.
Salomaa, A. (1973), Formal Languages. Academic Press, New York.
COMBINATORICS ON WORDS
Tero Harju, University of Turku
harju@utu.fi
1. Defect theorem
2. Critical factorization theorem
3. Ehrenfeucht’s conjecture
References
Lothaire, M. (1983), Combinatorics on Words. Addison-Wesley, Reading,
MA.
Lothaire, M. (2002), Algebraic Combinatorics of Words. Cambridge
University Press, Cambridge.
VARIETIES OF FORMAL LANGUAGES
Jean-Éric Pin, CNRS and University Paris 7
jean-eric.pin@liafa.jussieu.fr
1
1. Rational and recognizable sets
2. Finite automata and recognizable sets
3. Automata and semigroups
4. A bit of history...
5. Star-free languages
6. Piecewise testable languages
7. Locally testable languages
8. Varieties, Eilenberg's theorem
9. Elementary semigroup theory
10. More examples of varieties
11. Overview of recent advances
References
To be distributed.
REGULAR GRAMMARS
Masami Ito, Kyoto Sangyo University
ito@ksuvx0.kyoto-su.ac.jp
1.
2.
3.
4.
5.
6.
Regular grammars and languages
Syntactic congruences
Deterministic and nondeterministic automata
Operations on languages
Shuffle products and closures
Directable automata and languages
References
Hopcroft, J.E. & J.D. Ullman (1979), Introduction to Automata Theory,
Languages and Computation. Addison-Wesley, Reading, MA.
Ito, M. (2004), Algebraic Theory of Automata and Languages. World
Scientific, Singapore.
Salomaa, A. (1981), Jewels of Formal Language Theory. Computer Science
Press, Rockville, MD.
CONTEXT-FREE GRAMMARS
Manfred Kudlek, University of Hamburg
kudlek@informatik.uni-hamburg.de
1.
2.
3.
4.
5.
6.
7.
8.
9.
Normal forms
Iteration lemmata
Derivation trees, ambiguity
Relation to pushdown automata
Deterministic context-free languages
Complexity of analysis
Decidability problems
Closure properties
Algebraic characterization
References
2
Harrison, M.A. (1978), Introduction to Formal Language Theory. AddisonWesley, Reading, MA.
Hopcroft, J.E. & J.D. Ullman (1979), Introduction to Automata Theory,
Languages and Computation. Addison-Wesley, Reading, MA.
Salomaa, A. (1973), Formal Languages. Academic Press, New York.
INFINITE WORDS
Juhani Karhumäki, University of Turku
karhumak@cs.utu.fi
1. Mechanisms to generate infinite words
2. Repetitions in infinite words and applications
3. Subword complexity of infinite words
References
Choffrut, C. & J. Karhumäki (1997), Combinatorics of words, in G.
Rozenberg & A. Salomaa, eds., Handbook of Formal Languages, vol. I: 329438. Springer, Berlin.
Fogg, P. (2002), Substitutions in Dynamics, Arithmetics and Combinatorics,
Lecture Notes in Mathematics 1794. Springer, Berlin.
Lothaire, M. (1983), Combinatorics on Words. Addison-Wesley, Reading,
MA.
Lothaire, M. (2002), Algebraic Combinatorics of Words. Cambridge
University Press, Cambridge.
MILDLY CONTEXT-SENSITIVE GRAMMARS
Henning Bordihn, University of Potsdam
henning@cs.uni-potsdam.de
1. Motivation, definitions and background
2. Tree-adjoining grammars and equivalent devices
3. Further approaches to mild context-sensitivity
References
Joshi, A.K. (1985), How much context-sensitivity is required to provide
reasonable structural descriptions: tree adjoining grammars, in D. Dowty, L.
Karttunen & A. Zwicky, eds., Natural Language Parsing: Psychological,
Computational, and Theoretical Perspectives: 206-250. Cambridge
University Press, Cambridge.
Joshi, A.K. & Y. Schabes (1997), Tree adjoining grammars, in G. Rozenberg
& A. Salomaa, eds., Handbook of Formal Languages, vol. 3: 69-124.
Springer, Berlin.
Kudlek, M., C. Martín-Vide, A. Mateescu & V. Mitrana (2003), Contexts and
the concept of mild context-sensitivity, Linguistics and Philosophy, 26: 703725.
Marcus, S. (1969), Contextual grammars and natural languages, in G.
Rozenberg & A. Salomaa, eds., Handbook of Formal Languages, vol. 2: 215235. Springer, Berlin.
Partee, B.H., A.G.B. ter Meulen & R.E. Wall (1990), Mathematical Methods
in Linguistics. Kluwer, Dordrecht.
3
Pullum, G.K. & G. Gazdar (1982), Natural languages and context-free
languages, Linguistics and Philosophy, 4: 471-504.
Roach, K. (1987), Formal properties of head grammars, in A. Manaster
Ramer, ed., Mathematics of Language: 293-347. John Benjamins,
Amsterdam.
Shieber, S.M. (1985), Evidence against the context-freeness of natural
language, Linguistics and Philosophy, 8: 333-343.
Steedman, M. (1985), Dependency and coordination in the grammar of
Dutch and English, Language, 61: 523-568.
Vijay-Shanker, K. & D.J. Weir (1994), The equivalence of four extensions of
context-free grammars, Mathematical Systems Theory, 87: 511-546.
FINITE AUTOMATA
Sheng Yu, University of Western Ontario, London ON, Canada
syu@csd.uwo.ca
1.
2.
3.
4.
5.
6.
7.
8.
9.
Deterministic and nondeterministic finite automata
Regular expressions
Automata minimization
State complexities of regular languages
Alternating finite automata
Equational representation of regular languages
Finite transducers and rational relations
Finite languages and cover automata
Fuzzy automata and fuzzy regular expressions
References
Berstel, J. (1979), Transductions and Context-free Languages. Teubner,
Stuttgart.
Campeanu, C., N. Sântean & S. Yu (2001), Minimal cover-automata for
finite languages, Theoretical Computer Science, 267: 3-16.
Fellah, A., H. Jürgensen & S. Yu (1990), Constructions on alternating finite
automata, International Journal of Computer Mathematics, 35(3-4): 117132.
Hopcroft, J.E. & J.D. Ullman (1979), Introduction to Automata Theory,
Languages and Computation. Addison-Wesley, Reading, MA.
Lewis, H.R. & C.H. Papadimitriou (1998), Elements of the Theory of
Computation, 2nd ed. Prentice-Hall, Englewood Cliffs, NJ.
Mateescu, A., A. Salomaa, K. Salomaa & S. Yu (1995), Lexical analysis with
a simple finite-fuzzy-automaton model, Journal of Universal Computer
Science, 1(5): 292-311.
Salomaa, A. (1969), Theory of Automata. Pergamon, Oxford.
Salomaa, A. (1985), Computation and Automata. Cambridge University
Press, Cambridge.
Szilard, A., S. Yu, K. Zhang & J. Shallit (1992), Characterizing regular
languages with polynomial densities, in I.M. Havel & V. Koubek, eds.,
Mathematical Foundations of Computer Science 1992, Lecture Notes in
Computer Science 629: 494-503. Springer, Berlin.
Wood, D. (1987), Theory of Computation. John Wiley, New York.
Yu, S. (1997), Regular languages, in G. Rozenberg & A. Salomaa, eds.,
Handbook of Formal Languages, vol. I: 41-110. Springer, Berlin.
4
Yu, S. (1999), State complexity of regular languages, Journal of Automata,
Languages and Combinatorics, 6(2): 221-233.
PUSHDOWN AUTOMATA
Hendrik Jan Hoogeboom, Leiden University
hoogeboo@liacs.nl
1.
2.
3.
4.
Acceptance by final state and by empty stack: equivalence
Equivalence of pushdown automata and context-free grammars
Determinism, real-time property
LL(1) parsing
References
Autebert, J.-M., J. Berstel & L. Boasson (1997), Context-free languages and
pushdown automata, in G. Rozenberg & A. Salomaa, eds., Handbook of
Formal Languages, vol. I. Springer, Berlin.
Hopcroft, J.E., R. Motwani & J.D. Ullman (2001), Introduction to Automata
Theory, Languages and Computation. Addison-Wesley, Reading, MA.
TURING MACHINES
Holger Petersen, University of Stuttgart
petersen@informatik.uni-stuttgart.de
To be announced.
COMPUTATIONAL COMPLEXITY
Markus Holzer, Technical University of Munich
holzer@informatik.tu-muenchen.de
1. Basics in complexity theory: sequential classes, parallel classes
2. Fixed and general membership problems: Chomsky languages,
regular languages revisited, Lindenmayer languages, other formal
language classes
3. Some other problems: finiteness etc., counting problems
4. Operations on complexity classes
5. Auxiliary space bounded automata with abstract storage: pushdown
automata, variants of stack automata
References
Barrington, D.A. (1989), Bounded-width polynomial-size branching
programs recognize exactly those languages in {{m NC}^1}, Journal of
Computer and System Sciences, 38(1): 150-164.
Damm, C., M. Holzer & K.-J. Lange (1992), The parallel complexity of
iterated morphisms and the arithmetic of small numbers, in I.M. Havel & V.
Koubek, eds., Mathematical Foundations of Computer Science 1992, Lecture
Notes in Computer Science 629: 227-235. Springer, Berlin.
Holzer, M. (1996), On emptiness and counting for alternating finite
automata, in J. Dassow, G. Rozenberg & A. Salomaa, eds., Developments in
Language Theory II: At the Crossroads of Mathematics, Computer Science
and Biology: 88-97. World Scientific, Singapore.
5
Holzer, M. & K.-J. Lange (1993), On the complexities of linear LL(1) and
LR(1) grammars, in Z. Ésik, ed., Fundamentals of Computation Theory
1993, Lecture Notes in Computer Science 710: 299-308. Springer, Berlin.
Holzer, M. & K.-J. Lange (1997), On the complexity of iterated insertions, in
G. Păun & A. Salomaa, eds., New Trends in Formal Languages: Control,
Cooperation, and Combinatorics, Lecture Notes in Computer Science 1218:
440-453. Springer, Berlin.
Lange, K.-J. (1996), Complexity and structure in formal language theory,
Fundamenta Informaticae, 25(3-4): 327-352.
Monien, B. (1981), On the LBA problem, in F. Gécseg, ed., Fundamentals of
Computation Theory 1981, Lecture Notes in Computer Science 117: 265280. Springer, Berlin.
Monien, B. & I. Sudborough (1980), The interface between language theory
and complexity theory, in R.V. Book, ed., Formal Languages: Perspectives
and Open Problems: 287-324. Academic Press, New York.
Papadimitriou, C.H. (1994), Computational Complexity. Addison-Wesley,
Reading, MA.
Sudborough, I.H. (1975), A note on tape-bounded complexity classes and
linear context-free languages, Journal of the Association for Computing
Machinery, 22(4): 499-500.
Sudborough, I.H. (1976), The complexity of the membership problem for
some extensions of context-free languages, Computing Reviews, 19(5):
191-215.
PATTERNS
Kai Salomaa, Queen’s University, Kingston ON, Canada
ksalomaa@cs.queensu.ca
1.
2.
3.
4.
5.
Pattern languages, E-patterns, NE-patterns
Equivalence and inclusion problems, connection to rewriting systems
Ambiguity in patterns
Pattern systems
Pattern selector grammars
References
Angluin, D. (1980), Finding patterns common to a set of strings, Journal of
Computer and System Sciences, 21: 46-62.
Goldman, S. & S. Kwek (2002), On learning unions of pattern languages
and tree patterns in the mistake bound model, Theoretical Computer
Science, 288: 237-254.
Jiang, T., E. Kinber, A. Salomaa, K. Salomaa & S. Yu (1994), Pattern
languages with and without erasing, International Journal of Computer
Mathematics, 50: 147-163.
Jiang, T., A. Salomaa, K. Salomaa & S. Yu (1995), Decision problems for
patterns, Journal of Computer and System Sciences, 50: 53-63.
Marron, A. & K.-I. Ko (1987), Identification of pattern languages from
examples and queries, Information and Computation, 74: 91-112.
Mateescu, A. & A. Salomaa (1994), Finite degrees of ambiguity in pattern
languages, Theoretical Informatics and Applications, 28: 233-253.
Mitrana, V. (1999), Patterns and languages: an overview, Grammars, 2(2):
149-173.
6
Ohlebusch, E. & E. Ukkonen (1997), On the equivalence problem for Epattern languages, Theoretical Computer Science, 186: 231-248.
DESCRIPTIONAL COMPLEXITY OF AUTOMATA AND GRAMMARS
Detlef Wotschke, University of Frankfurt
wotschke@psc.informatik.uni-frankfurt.de
1. Major results in descriptional complexity of automata and grammars
2. Relationship between the use of limited resources (like
nondeterminism, ambiguity, lookahead, etc.) and their effect on the
smallest possible descriptions or representations of objects such as
finite automata, probabilistic automata, pushdown automata,
context-free grammars, etc.
References
Bucher, W., H.A. Maurer, K. Culik, II & D. Wotschke (1981), Concise
description of finite languages, Theoretical Computer Science, 14(3): 227246.
Geller, M.M., H.B. Hunt, III, T.G. Szymanski & J.D. Ullman (1977), Economy
of description of parsers, DPDA's, and PDA's, Theoretical Computer Science,
4(2): 143-153.
Goldstine, J., C.M.R. Kintala & D. Wotschke (1990), On measuring
nondeterminism in regular languages, Information and Computation, 86(2):
179-194.
Goldstine, J., H. Leung & D. Wotschke (1992), On the relation between
ambiguity and nondeterminism in finite automata, Information and
Computation, 100(2): 261-270.
Goldstine, J., H. Leung & D. Wotschke (1997), Measuring nondeterminism
in pushdown automata, in R. Reischuk & M. Morvan, eds., Theoretical
Aspects of Computer Science 1997, Lecture Notes in Computer Science
1200: 295-306. Springer, Berlin.
Goldstine, J., J.K. Price & D. Wotschke (1982), A pushdown automaton or a
context-free grammar: which is more economical?, Theoretical Computer
Science, 18(1): 33-40.
Goldstine, J., J.K. Price & D. Wotschke (1982), On reducing the number of
states in a PDA, Mathematical Systems Theory, 15(4): 315-321.
Goldstine, J., J.K. Price & D. Wotschke (1993), On reducing the number of
stack symbols in a PDA, Mathematical Systems Theory, 26(4): 313-326.
Hartmanis, J. (1980), On the succinctness of different representations of
languages, SIAM Journal on Computing, 9(1): 114-120.
Herzog, C. (1997), Pushdown automata with bounded nondeterminism and
bounded ambiguity, Theoretical Computer Science, 181(1): 141-157.
Kappes, M. (2000), Descriptional complexity of deterministic finite automata
with multiple initial states, Journal of Automata, Languages and
Combinatorics, 5(3): 269-278.
Kintala, C.M.R. (1978), Refining nondeterminism in context-free languages,
Mathematical Systems Theory, 12(1): 1-8.
Kintala, C.M.R., K.-Y. Pun & D. Wotschke (1993), Concise representations of
regular languages by degree and probabilistic finite automata, Mathematical
Systems Theory, 26(4): 379-395.
7
Kintala, C.M.R. & D. Wotschke (1980), Amounts of nondeterminism in finite
automata, Acta Informatica, 13(2): 199-204.
Kintala, C.M.R. & D. Wotschke (1986), Concurrent conciseness of degree,
probabilistic, nondeterministic and deterministic finite automata, in B.
Monien & G. Vidal-Naquet, eds., Theoretical Aspects of Computer Science
1986, Lecture Notes in Computer Science 210: 291-305. Springer, Berlin.
Leung, H. (1998), On finite automata with limited nondeterminism, Acta
Informatica, 35(7): 595-624.
Leung, H. (2000), On a family of nondeterministic finite automata, Journal
of Automata, Languages and Combinatorics, 5(3): 235-244.
Leung, H. & D. Wotschke (2000), On the size of parsers and LR(k)grammars, Theoretical Computer Science, 242(1-2): 59-69.
Malcher, A. (2001), Descriptional complexity of cellular automata and
decidability questions, in J. Dassow & D. Wotschke, eds., Proceedings of the
Third International Workshop on Descriptional Complexity of Automata,
Grammars and Related Structures (DCAGRS 2001): 123-132. Otto-vonGuericke-Universität Magdeburg, Magdeburg.
Meyer, A.R. & M.J. Fischer (1971), Economy of description by automata,
grammars, and formal systems, Proceedings of the IEEE Twelfth Annual
Symposium on Switching and Automata Theory. IEEE: 188-191.
Salomaa, K. & S. Yu (1991), Degrees of nondeterminism for pushdown
automata, in L. Budach, ed., Fundamentals of Computation Theory 1991,
Lecture Notes in Computer Science 529: 380-389. Springer, Berlin.
Salomaa, K. & S. Yu (1994), Measures of nondeterminism for pushdown
automata, Journal of Computer and System Sciences, 49(2): 362-374.
Valiant, L.G. (1976), A note on the succinctness of descriptions of
deterministic languages, Information and Control, 32(2): 139-145.
AUTOMATA AND LOGIC
Franz Baader, Technical University of Dresden
baader@tcs.inf.tu-dresden.de
To be announced.
DECISION PROBLEMS OF RATIONAL RELATIONS
Christian Choffrut, CNRS and University Paris 7
christian.choffrut@liafa.jussieu.fr
1. Recognizable and rational families of relations in free monoids
2. Undecidable problems (the non-unary case)
3. Decidable problems (the unary case)
References
Berstel, J. (1979), Transductions and Context-Free Languages. Teubner,
Stuttgart.
Sakarovitch, J. (2003), Éléments de Théorie des Automates. Vuibert, Paris.
TWO-DIMENSIONAL LANGUAGES
Kenichi Morita, Hiroshima University
morita@iec.hiroshima-u.ac.jp
8
1. Basics for two-dimensional languages
2. Two-dimensional automata
3. Two-dimensional grammars
References
Blum, M. & C. Hewitt (1967), Automata on a two-dimensional tape, in
Proceedings of the IEEE Eighth Annual Symposium on Switching and
Automata Theory. IEEE: 155-160.
Giammarresi, D. & A. Restivo (1997), Two-dimensional languages, in G.
Rozenberg & A. Salomaa, eds., Handbook of Formal Languages, 3 vols.
Springer, Berlin.
Inoue, K. & I. Takanami (1989), A survey of two-dimensional automata
theory, in J. Dassow & J. Kelemen, eds., Machines, Languages, and
Complexity, Lecture Notes in Computer Science 381: 72-91. Springer,
Berlin.
Rosenfeld, A. (1979), Picture Languages. Academic Press, New York.
Wang, P.S.P., ed. (1989), Array Grammars, Patterns and Recognizers.
World Scientific, Singapore 1989.
Yamamoto, Y., K. Morita & K. Sugata (1989), Context-sensitivity of twodimensional regular array grammars, International Journal of Pattern
Recognition and Artificial Intelligence, 3: 295-319.
GRAMMARS WITH REGULATED REWRITING
Jürgen Dassow, University of Magdeburg
dassow@iws.cs.uni-magdeburg.de
1.
2.
3.
4.
5.
6.
Background and motivation. Regulation by context-conditions
Regulation by prescribed sequences of rules
Further regulations
Comparison of generative power
Decidability, computational and syntactic complexity
Some further properties
References
Abraham, S. (1965), Some questions of phrase-structure grammars,
Computational Linguistics, 4: 61-70.
Aho, A.V. (1968), Indexed grammars: an extension of context-free
grammars, Journal of the Association for Computing Machinery, 15: 647671.
Dassow, J. & G. Păun (1989), Regulated Rewriting in Formal Language
Theory. Springer, Berlin.
Dassow, J., G. Păun & G. Rozenberg (1997), Grammars with controlled
derivations, in G. Rozenberg & A. Salomaa, eds., Handbook of Formal
Languages, vol. II. Springer, Berlin.
Fris, I. (1968), Grammars with a partial ordering of the rules, Information
and Control, 12: 415-425.
Ginsburg, S. & E.H. Spanier (1968), Control sets on grammars,
Mathematical Systems Theory, 2: 159-177.
Greibach, S. & J.E. Hopcroft (1969), Scattered context grammars, Journal
of Computer and System Sciences, 3: 233-247.
9
Păun, G. (1980), A new generative device: valence grammars, Revue
Roumaine de Mathématiques Pures et Appliquées, 25: 911-924.
Rosenkrantz, D.J. (1969), Programmed grammars and classes of formal
languages, Journal of the Association for Computing Machinery, 16: 107131.
Salomaa, A. (1970), Periodically time-varying context-free grammars,
Information and Control, 17: 194-211.
Salomaa, A. (1973), Formal Languages. Academic Press, New York.
Siromoney, R. & K. Krithivasan (1974), Parallel context-free grammar,
Information and Control, 24: 155-162.
Walt, A.P.J. van der (1972), Random context languages, in C.V. Freiman,
J.E. Griffith & J.L. Rosenfeld, eds., Information Processing 71, vol. I. NorthHolland, Amsterdam.
GRAMMAR SYSTEMS
Erzsébet Csuhaj-Varjú, Hungarian Academy of Sciences, Budapest
csuhaj@sztaki.hu
Grammar systems is a recent active field of formal language theory,
providing syntactic models, frameworks and tools for describing and
studying multi-agent systems at the symbolic level. Several scientific areas
have inspired and influenced the developments in this theory: distributed
and decentralized artificial intelligence, distributed and parallel computing,
artificial life, molecular computing, robotics, ecology, sociology, etc.
Computer networks, parallel and distributed computer architectures,
distributed and cooperative text processing, natural language processing
are candidates for possible applications.
A grammar system consists of several language identifying devices
(language processors or linguistic agents) that jointly develop a common
symbolic environment (usually, a string or a finite set of strings) by
applying operations to it. The symbolic environment can be shared by the
components of the system, or it can be given in the form of a collection of
separated sub-environments, each belonging to a language processor. At
any moment in time, the state of the system is represented by the current
string describing the environment (collection of strings of the subenvironments). The functioning of the system is realized by changes in its
states. Depending on the variant of multi-agent system that the actual
grammar system represents, in addition to performing operations, the
language processors are allowed to communicate with each other. The
behaviour of the grammar system can be characterized by the set of
sequences of environmental states following each other, starting from an
initial state, or by the set of all environmental states originating from an
initial state and satisfying some criteria (final states).
The aim of the course is to give a picture about the research directions in
the area, without the aim of completeness, by presenting some important
frameworks, models, and results.
1. Grammar systems: the theory
10
A short introduction about the motivations, preliminaries, and background
information concerning grammar systems theory: aims and objectives, main
research directions and perspectives of the area.
2. Cooperating distributed grammar systems
Cooperating distributed (CD) grammar systems are syntactic models of the
well-known blackboard type problem solving systems from artificial
intelligence, where the cooperating problem solving agents are represented
by grammars which jointly generate words of a common language,
corresponding to the set of problem solutions. The actual contents of the
global database, the blackboard, used in the course of the problem solving
process, is represented by the actual sentential form in generation. We
discuss the most important variants of these systems and their cooperation
protocols, the generative power and the descriptional complexity of these
constructs. We demonstrate how notions as competence, fairness,
incomplete information processing can be represented in terms of CD
grammar systems.
3. Colonies
Colonies can be considered as grammatical models of communities of very
simple, pure reactive agents with emergent behaviour. We discuss the basic
variants of these constructions, with special emphasis on the notion of
emergence in terms of formal language theory.
4. Eco-grammar systems
Eco-grammar systems are formal language theoretic models of artificial life,
grammatical frameworks for describing the behaviour of communities of
dynamically changing (developing) agents which are in interaction with their
shared dynamically changing environment. We introduce the basic variants
of eco-grammar systems and discuss their important properties, in
particular the team behaviour of the agents. We also demonstrate how
characteristics of life as birth, death, overpopulation, pollution can be
expressed in terms of eco-grammar systems.
5. Networks of language processors
A network of language processors is a virtual graph (a network) with a
language processor (a grammar) and a set (a multiset) of strings in each
node. The language processors perform operations on the strings that can
be found at the corresponding node and then communicate some of the
obtained words to each other, according to a protocol. We discuss the two
main variants of these constructions: parallel communicating grammar
systems where communication is done by request, and parallel
communicating grammar systems where communication is done by
command. We describe their computational power and descriptional
complexity, and demonstrate how phenomena typical in networks can be
modelled by these systems. We also present examples for bio-inspired
networks of language processors.
11
References
Csuhaj-Varjú, E., J. Dassow, J. Kelemen & G. Păun (1994), Grammar
Systems: A Grammatical Approach to Distribution and Cooperation. Gordon
and Breach, London.
Dassow, J., G. Păun & G. Rozenberg (1997), Grammar systems, in G.
Rozenberg & A. Salomaa, eds., Handbook of Formal Languages, vol II: 155213. Springer, Berlin.
Articles referred in E. Csuhaj-Varjú & György Vaszil, An annotated
bibliography of grammar systems: http://www.sztaki.hu/mms/bib.html
PARALLEL GRAMMARS
Henning Fernau, University of Tübingen
fernau@informatik.uni-tuebingen.de
1.
2.
3.
4.
Lindenmayer systems
Indian parallel grammars
(Uniformly) limited Lindenmayer systems
Interfaces with regulated rewriting and grammar systems: scattered
context grammars and parallel communicating grammar systems
References
Herman, G.T. & G. Rozenberg (1975), Developmental Systems and
Languages. North-Holland, Amsterdam.
Prusinkiewicz, P. & A. Lindenmayer (1990), The Algorithmic Beauty of
Plants. Springer, New York.
Rozenberg, G. & A. Salomaa (1980), The Mathematical Theory of L
Systems. Academic Press, New York.
CONTEXT-SENSITIVE GRAMMARS
Victor Mitrana, Rovira i Virgili University, Tarragona
vmi@urv.net
1.
2.
3.
4.
5.
6.
7.
When and why context-freeness is not sufficient
Normal forms for context-sensitive grammars
Workspace theorem
Linear bounded automata. The LBA problem
Closure properties
Decidable properties
Context-sensitive grammars generating context-free languages
References
Hopcroft, J.E. & J.D. Ullman (1979), Introduction to Automata Theory,
Languages and Computation. Addison-Wesley, Reading, MA.
Immerman, N. (1988), Nondeterministic space is closed under
complementation, SIAM Journal of Computing, 17(5): 935-938.
Kuroda, S.Y. (1964), Classes of languages and linear bounded automata,
Information and Control, 7: 207-223.
Rozenberg, G. & A. Salomaa, eds. (1997), Handbook of Formal Languages,
3 vols. Springer, Berlin.
12
Salomaa, A. (1973), Formal Languages. Academic Press, New York.
Szelepcseny, R. (1988), The method of forced enumeration for
nondeterministic automata, Acta Informatica, 26: 279-284.
TREE AUTOMATA AND TREE LANGUAGES
Magnus Steinby, University of Turku
steinby@utu.fi
1. Finite tree automata and regular tree languages
2. Tree transducers and tree transformations
3. Tree automata and term rewriting
References
Gécseg, F. & M. Steinby (1984), Tree Automata. Akadémiai Kiadó,
Budapest.
Gécseg, F. & M. Steinby (1997), Tree languages, in G. Rozenberg & A.
Salomaa, eds., Handbook of Formal Languages, vol. III: 1-68. Springer,
Berlin.
Steinby, M., lecture notes to be prepared for the course.
TREE TRANSDUCERS
Zoltán Fülöp, University of Szeged
fulop@inf.u-szeged.hu
By a ‘tree’ we mean a term over a ranked alphabet. A tree transducer is a
finite state device which computes a tree transformation, i.e. a binary
relation over trees. Hence, tree transducers generalize sequential machines
and serve as formal models of the syntax-directed translation.
There are several tree transducer models. However, in this lecture series we
consider only the most fundamental ones: the classical bottom-up and topdown tree transducers [1], attributed tree transducers [3,6] and macro tree
transducers [2,6].
In the first lecture, we consider bottom-up and top-down tree transducers
and their restricted versions. We compare the computation power of the
different tree transducer models by giving inclusion diagrams of the tree
transformation classes computed by them.
In the second lecture, we deal with the composition theory and the
decomposition theory of tree transducers. We find tree transducer classes
C, D and E such that the computation performed by the consecutive
application of a tree transducer of type C and a tree transducer of type D
can be simulated by a single tree transducer of type E (composition theory).
Vice versa, we are interested in tree transducer classes E, C and D which
have the following property: any tree transformation computed by a tree
transducer of type E can be decomposed into two tree transformations of
type C and D (decomposition theory). We give the full description of
monoids generated by tree transformation classes in terms of inclusion
diagrams and convergent string rewrite systems.
13
In the third lecture, we generalize top-down tree transducers. We introduce
macro tree transducers and attributed tree transducers. We compare their
computation power and give some composition and decomposition results.
The text of the above three lectures can be found in [4].
In the exercise session, we give examples of the tree transducer models
and the constructions applied in the lectures.
In the paper session, we will consider recent research papers as well as
open problems concerning tree transducers.
References
[1] Engelfriet, J. (1975), Bottom-up and top-down tree transducers - A
comparison, Mathematical Systems Theory, 9: 198-231.
[2] Engelfriet, J. & H. Vogler (1985), Macro tree transducers, Journal of
Computer and System Sciences, 31: 95-125.
[3] Fülöp, Z. (1981), On attributed tree transducers, Acta Cybernetica, 5:
261-279.
[4] Fülöp, Z. (2004), A short introduction to tree transducers, Technical
Report 30/04, Research Group on Mathematical Linguistics, Universitat
Rovira i Virgili, Tarragona.
[5] Fülöp, Z. & S. Vagvölgyi (1992), Decidability of the inclusion in monoids
generated by tree transformation classes, in M. Nivat & A. Podelski, eds.,
Tree Automata and Languages: 381-408, Elsevier Science, Amsterdam.
[6] Fülöp, Z. & H. Vogler (1998), Syntax-Directed Semantics - Formal
Models Based on Tree Transducers. Springer, Berlin.
[7] Gécseg, F. & M. Steinby (1984), Tree Automata. Akadémiai Kiadó,
Budapest.
[8] Gécseg, F. & M. Steinby (1997), Tree languages, in G. Rozenberg & A.
Salomaa, eds., Handbook of Formal Languages, vol. III: 1-68. Springer,
Berlin.
FORMAL LANGUAGES AND CONCURRENT SYSTEMS
Jetty Kleijn, Leiden University
kleijn@liacs.nl
1.
2.
3.
4.
Introduction
Traces
Elementary net systems
Generalizations
References
Diekert, V. & G. Rozenberg, eds. (1995), The Book of Traces. World
Scientific, Singapore.
Hoogers, P.W., H.C.M. Kleijn & P.S. Thiagarajan (1995), A trace semantics
for Petri nets, Information and Computation, 117: 98-114.
Janicki, R. & M. Koutny (1995), Semantics of inhibitor nets, Information and
Computation, 123: 1-16.
Mazurkiewicz, A. (1986), Trace theory, in W. Brauer, W. Reisig & G.
14
Rozenberg, eds., Petri Nets: Applications and Relationships to Other Models
of Concurrency, Lecture Notes in Computer Science 255: 279-324.
Springer, Berlin.
Rozenberg, G. & J. Engelfriet (1998), Elementary net systems, in W. Reisig
& G. Rozenberg, eds., Lectures on Petri Nets I: Basic Models, Lecture Notes
in Computer Science 1491: 12-121. Springer, Berlin.
GRAPH GRAMMARS AND GRAPH TRANSFORMATION
Hans-Jörg Kreowski, University of Bremen
kreo@informatik.uni-bremen.de
1. Motivating examples of graphs, graph languages, graph properties,
graph-processing problems, and graph algorithms
2. Basic features of rule-based graph transformation
3. Graph transformation units
4. Context-free graph grammars
5. Parallelism and concurrency
6. Computing and modeling by graph transformation
References
Rozenberg, G., ed. (1997), Handbook of Graph Grammars and Computing
by Graph Transformation, vol. I: Foundations. World Scientific, Singapore.
[In particular: Chapter 1: J. Engelfriet & G. Rozenberg, Node replacement
graph grammars: 1-94. Chapter 2: F. Drewes, H.-J. Kreowski & A. Habel,
Hyperedge replacement graph grammars: 95-162.]
Ehrig, H., G. Engels, H.-J. Kreowski & G. Rozenberg, eds. (1999), Handbook
of Graph Grammars and Computing by Graph Transformation, vol. II:
Applications, Languages and Tools. World Scientific, Singapore. [In
particular: H.-J. Kreowski & S. Kuske, Graph transformation units and
modules: 607-638.]
Ehrig, H., H.-J. Kreowski, U. Montanari & G. Rozenberg, eds. (1999),
Handbook of Graph Grammars and Computing by Graph Transformation,
vol. III: Concurrency, Parallelism, and Distribution. World Scientific,
Singapore.
PETRI NET THEORY AND ITS APPLICATIONS
Hsu-Chun Yen, National Taiwan University, Taipeh
yen@cc.ee.ntu.edu.tw
Petri nets represent one of the most important mathematical models for
describing concurrent systems and their behaviors. To understand the basic
concepts, analytical techniques, capabilities and limitations of Petri nets,
this short course focuses on Petri nets, their analytical techniques and
properties from an automata/complexity viewpoint.
1. Introduction to Petri nets: basic notations and definitions, capabilities
and limitations of Petri nets, restricted and extended classes of Petri
nets
2. Analytical techniques for Petri nets: reachability analysis, coverability
graph, matrix equation, structural analysis
15
3. Complexity/decidability issues of Petri net problems: upper and lower
bounds for various Petri net problems, including reachabiltiy,
boundedness, equivalence and containment, model checking, and
more
4. Petri net languages: various Petri net languages and their closure
properties, iteration lemma
5. Applications of Petri net theory: applications in supervisory control,
membrane computing, and more
References
Desel, J. & J. Esparza (1995), Free Choice Petri Nets. Cambridge University
Press, Cambridge.
Esparza, J. (1996), Decidability and complexity of Petri net problems: an
introduction, in W. Reisig & G. Rozenberg, eds., Lectures on Petri Nets I:
Basic Models, Lecture Notes in Computer Science 1491: 374-428. Springer,
Berlin.
Howell, R., D. Huynh, L. Rosier & H. Yen (1986), Some complexity bounds
for problems concerning finite and 2-dimensional vector addition systems
with states, Theoretical Computer Science, 46(2-3): 107-140.
Howell, R., L. Rosier & H. Yen (1991), A taxonomy of fairness and temporal
logic problems for Petri nets, Theoretical Computer Science, 82: 341-372.
Murata, T. (1989), Petri-nets: properties, analysis and applications,
Proceedings of the IEEE, 77(4): 541-580.
Peterson, J.L. (1981), Petri Net Theory and the Modeling of Systems.
Prentice-Hall, Englewood Cliffs, NJ.
Reisig, W. & G. Rozenberg, eds. (1998), Lectures on Petri Nets I: Basic
Models and II: Applications, Lecture Notes in Computer Science 1491/1492.
Springer, Berlin.
Rosier, L. & H. Yen (1986), A multiparameter analysis of the boundedness
problem for vector addition systems, Journal of Computer and System
Sciences, 32(1): 105-135.
Yen, H. (1996), On the regularity of Petri net languages, Information and
Computation, 124(2): 168-181.
TREE ADJOINING GRAMMARS
James Rogers, Earlham College, Richmond IN, United States
jrogers@cs.earlham.edu
1. Linguistic motivation: extended domain of locality, factoring recursion
2. Formal aspects: substitution and adjunction, derivation trees and
derived sets, CFL and TAL, TAL closure results, recognizable tree sets
and TAG tree sets, TAG tree set closure results, pumping lemma,
independence of paths, MCTAG (variations, generative capacity),
EPDA, LCFRS (head grammars, linear indexed grammar, CCG), multidimensional tree automata (CLH), FTAG, lexicalization (LTAG)
3. Linguistic aspects: EDL revisited, lexicalization revisited, FTAG
revisited, the condition on elementary tree minimality, dependency,
coordination
4. Synchronous TAGs: translation, generation
5. Syntax/semantics interface
6. Statistical approaches: supertagging
16
References
Frank, R.E. (1992), Syntactic locality and tree adjoining grammar:
grammatical, acquisition and processing perspectives, Department of
Computer and Information Science, University of Pennsylvania.
Joshi, A.K. & Y. Schabes (1997), Tree-adjoining grammars, in G. Rozenberg
& A. Salomaa, eds., Handbook of Formal Languages, vol. 3. Springer,
Berlin.
Joshi, A.K., K. Vijay-Shanker & D. Weir (1991), The convergence of mildly
context-sensitive grammar formalisms, in P. Sells, S. Shieber & T. Wasow,
eds., Foundational Issues in Natural Language Processing: 31-81. MIT
Press, Cambridge, MA.
Kroch, A.S. & A.K. Joshi (1985), Linguistic relevance of tree adjoining
grammars, Department of Computer and Information Science, University of
Pennsylvania, MS-CIS-85-18.
Vijay-Shanker, K. (1987), A study of tree adjoining grammars, Department
of Computer and Information Science, University of Pennsylvania.
Vijay-Shanker, K. & A.K. Joshi (1985), Some computational properties of
tree adjoining grammars, in Proceedings of the 23rd Annual Meeting of the
Association for Computational Linguistics. ACL: 82-93.
Vijay-Shanker, K., D.J. Weir & A.K. Joshi (1987), Characterizing structural
descriptions produced by various grammatical formalisms, in Proceedings of
the 25th Annual Meeting of the Association for Computational Linguistics.
ACL: 104-111.
Weir, D.J. (1988), Characterizing mildly context-sensitive grammar
formalisms, Department of Computer and Information Science, University of
Pennsylvania.
Weir, D.J. (1992), Linear context-free rewriting systems and deterministic
tree-walking transducers, in Proceedings of the 30th Annual Meeting of the
Association for Computational Linguistics. ACL: 136-143.
Weir, D.J., K. Vijay-Shanker & A.K. Joshi (1986), The relationship between
tree adjoining grammars and head grammars, in Proceedings of the 24th
Annual Meeting of the Association for Computational Linguistics. ACL: 6774.
RESTARTING AUTOMATA
Friedrich Otto, University of Kassel
otto@theory.informatik.uni-kassel.de
1. Restarting automata: motivation, definitions and basic properties.
Analysis by reduction: a motivation from linguistics. The RRWWautomaton. Restricted types of RRWW-automata. Error preserving
property, correctness preserving property, pumping lemma. An
RRWW-automaton for Lcopy := {w#w# | w ε {a, b}*}. A
characterization for the use of auxiliary symbols
2. Monotone restarting automata. Monotonicity for restarting automata.
Decidability of monotonicity. A characterization of the context-free
languages by monotone RWW- and RRWW- automata. A
characterization of the deterministic context-free languages by
various types of monotone deterministic restarting automata. The
taxonomy of monotone restarting automata
17
3. Deterministic restarting automata. The Church-Rosser languages. The
growing context-sensitive languages. The shrinking two-pushdown
automaton. A characterization of the Church-Rosser languages by the
deterministic RWW- and RRWW-automata. The taxonomy of
deterministic restarting automata
4. Nondeterministic restarting automata. The Gladkij language LGl :=
{w#wR#w | w ε {a, b}*}. An RWW-automaton for the Gladkij
language. Weak monotonicity for restarting automata. A
characterization of the growing context-sensitive languages by the
weakly monotone RWW- and RRWW-automata. The computational
power of nondeterministic restarting automata. The taxonomy of
nondeterministic restarting automata
5. Left-monotonicity. Left-monotonicity for restarting automata.
Shrinking (that is, weight-reducing) restarting automata. The power
of left-monotone deterministic restarting automata. A
characterization of the context-free languages by various types of
left-monotone nondeterministic restarting automata. The taxonomy
of left-monotone restarting automata
6. Degrees of (non-)monotonicity. A generalization of monotonicity: jmonotonicity and j-left-monotonicity. Hierarchy results with respect
to the degree j of monotonicity. Hierarchy results with respect to the
degree j of left-monotonicity. Hierarchy results with respect to the
degree of weak monotonicity. Open problems and directions for
further research
References
Jančar, P., F. Mráz, M. Plátek & J. Vogel (1995), Restarting automata, in H.
Reichel, eds., Fundamentals of Computation Theory 1995, Lecture Notes in
Computer Science 965: 283-292. Springer, Berlin.
Jančar, P., F. Mráz, M. Plátek & J. Vogel (1997), On restarting automata
with rewriting, in G. Păun & A. Salomaa, eds., New Trends in Formal
Languages, Lecture Notes in Computer Science 1218: 119-136. Springer,
Berlin.
Jančar, P., F. Mráz, M. Plátek & J. Vogel (1999), On monotonic automata
with a restart operation, Journal of Automata, Languages and
Combinatorics, 4: 287-311.
Jurdziński, T., K. Loryś, G. Niemann & F. Otto (2001), Some results on
RRW- and RRWW-automata and their relationship to the class of growing
context-sensitive languages, Mathematische Schriften Kassel, 14/01. Also:
Journal of Automata, Languages and Combinatorics, to appear.
Komorowski, J., Z. Pawlak, L. Polkowski & A. Skowron (1998), Rough sets:
a tutorial, in S.K. Pal & A. Skowron, eds., Rough-Fuzzy Hybridization: A New
Trend in Decision-Making: 3-98. Springer, Singapore.
Mráz, F. & F. Otto (2003), Hierarchies of weakly monotone restarting
automata, Mathematische Schriften Kassel, 8/03.
Niemann, G. & F. Otto (2000), Restarting automata, Church-Rosser
languages, and representations of r.e. languages, in G. Rozenberg & W.
Thomas, eds., Developments in Language Theory: Foundations,
Applications, and Perspectives: 103-114. World Scientific, Singapore.
18
Niemann, G. & F. Otto (2003), Further results on restarting automata, in M.
Ito & T. Imaoka, eds., Words, Languages and Combinatorics III: 352-369.
World Scientific, Singapore.
Otto, F. (2003), Restarting automata and their relations to the Chomsky
hierarchy, in Z. Ésik & Z. Fülöp, eds., Developments in Language Theory
2003, Lecture Notes in Computer Science 2710: 55-74. Springer, Berlin.
Otto, F. & T. Jurdziński (2003), On left-monotone restarting automata,
Mathematische Schriften Kassel, 17/03.
Plátek, M., F. Otto, F. Mráz & T. Jurdziński (2003), Restarting automata and
variants of j-monotonicity, Mathematische Schriften Kassel, 9/03.
CONTEXTUAL GRAMMARS
Carlos Martín-Vide, Rovira i Virgili University, Tarragona
carlos.martin@urv.net
1. Basic classes of contextual grammars: generative power,
characterizations, closure properties, decidability properties,
descriptional complexity, parsing complexity, ambiguity
2. Contextual automata
3. Bracketed and structured contextual grammars
4. Variants of using selectors: restricted selection, maximal/minimal use
of selectors
5. Derivation modes: leftmost derivation, parallel derivation, multidimensional contexts, derivation based on patterns
6. Insertion grammars
References
Dassow, J. & V. Mitrana (1998), The degree of parallelism in contextual
grammars with the maximal competence strategy, in C. Martín-Vide, ed.,
Mathematical and Computational Analysis of Natural Language: 3-16. John
Benjamins, Amsterdam.
Ehrenfeucht, A., G. Păun & G. Rozenberg (1997), Contextual grammars and
formal languages, in G. Rozenberg & A. Salomaa, eds., Handbook of Formal
Languages, vol. II: 237-294. Springer, Berlin.
Ilie, L. (1997), Some recent results on contextual languages, Bulletin of the
European Association for Theoretical Computer Science, 62: 176-193.
Kappes, M. (1998), On the generative capacity of bracketed contextual
grammars, Grammars, 1(2): 91-101.
Marcus, S. (1969), Contextual grammars, Revue Roumaine de
Mathématiques Pures et Appliquées, 14: 1525-1534.
Marcus, S. (1997) Contextual grammars and natural languages, in G.
Rozenberg & A. Salomaa, eds., Handbook of Formal Languages, vol. II:
215-235. Springer, Berlin.
Martín-Vide, C., A. Mateescu, J. Miquel-Vergés & G. Păun (1995), Internal
contextual grammars: minimal, maximal and scattered use of selectors, in
M. Koppel & E. Shamir, eds., Proceedings of The Fourth Bar-Ilan
Symposium on Foundations of Artificial Intelligence. Focusing on Natural
Languages and Artificial Intelligence - Philosophical and Computational
Aspects: 159-168. AAAI Press, Menlo Park, CA.
Martín-Vide, C., J. Miquel-Vergés & G. Păun (1996), Contextual automata,
ms.
19
Martín-Vide, C. & G. Păun (1998), Structured contextual grammars,
Grammars, 1(1): 33-55.
Mitrana, V. (1995), Contextual insertion and deletion, in G. Păun, ed.,
Mathematical Linguistics and Related Topics: 271-278. The Publishing
House of the Romanian Academy, Bucharest.
Mitrana, V. (1998), Chomsky-Schützenberger type characterizations based
on contextual languages, Grammars, 1(2), 167-176.
Păun, G. (1997), Marcus Contextual Grammars. Kluwer, Dordrecht.
20