Computational Modeling and Simulation of
Spatiotemporal Characteristics of Crime in
Urban Environments
Uwe Glässer
Software Technology Lab
School of Computing Science
Simon Fraser University
glaesser@cs.sfu.ca
Specification technology
Software Technology Lab @ SFU
Abstract State Machines

Rigorous modeling and analysis of complex
computational systems

Constructive approach for





Requirements analysis
Design specification
Experimental validation
Formal verification
ASM Research Center (www.asmcenter.org)
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
2
Applications
Software Technology Lab @ SFU

Semantic foundations

Modeling complex distributed systems







Communications software
Web service architectures
System design languages
Software technology for Intelligent Systems
Computational criminology
Aviation security
Computational methods and tools

Uwe Glässer
Abstract executable specifications
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
3
CoreASM
Executable specifications
R. Farahbod, V. Gervasi and U. Glässer. CoreASM: An Extensible ASM Execution
Engine. To appear in Fundamenta Informatica 77 (1-2), pp. 71-103
Verification
Environment
Problem
…
Design
Abstract Software Model
CoreASM
Ground model
Refinement
Software Technology Lab @ SFU

ConstructionAsmL, XASM, …
Coding
Uwe Glässer
Implementation
Detailed ground model
Code
Graphical UI
Testing
Environment
Control API
CoreASM Engine
Abstract
Storage
Parser
Interpreter
Scheduler
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
4
Software Technology Lab @ SFU
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
5
Software Technology Lab @ SFU
A notorious problem
How can one cope with the notorious problem of
establishing the correctness and completeness of
abstract functional requirements in the design of discrete
dynamic systems prior to actually building a system?
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
6
Software Technology Lab @ SFU
Can any algorithm, never mind how abstract, be
modeled by a generalized machine very closely
and faithfully? ... If we stick to one abstract level
(abstracting from low-level details and being
oblivious to a possible higher-level picture) and if
the states of the algorithm reflect all the pertinent
information, then a particular small instruction set
suffices in all cases.
 Yuri Gurevich
Sequential ASMs
Parallel ASMs (synchronous)
Distributed ASMs (asynchronous)
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
7
Church-Turing thesis
Software Technology Lab @ SFU
Every computable function is Turing computable. (1936)
… can be calculated by an effective or mechanical method
not demanding any insight or ingenuity
Any algorithm can be simulated by a Turing machine
with only polynomial slowdown.
An algorithm can be given a precise meaning by a Turing machine.
Can one generalize Turing machines so that any algorithm,
never mind how abstract, can be modeled by a generalized
machine very closely and faithfully?
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
8
Software Technology Lab @ SFU
The ASM thesis
The ASM thesis is that any algorithm can be modeled at its
natural abstraction level by an appropriate ASM.
(Gurevich, 1985)
Sequential thesis:
Sequential ASMs capture sequential algorithms. (Gurevich, 2000)
Parallel thesis:
ASMs capture parallel algorithms. (Blass/Gurevich, 2003)
…?
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
9
Software Technology Lab @ SFU
Abstract state machine
An ASM is a virtual machine with abstract states,
combining two fundamental abstraction principles:
first-order structures + state transition systems.
Vocabulary
Initial states
Program
f(t1,t2,…,tn): t0
if C then R1 else R2
…
do-in-parallel
R1
Rk
forall x in S
R(x)
choose x in S: (x)
R(x)
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
10
Computation
Software Technology Lab @ SFU
1
2
i 1
X0  X1  X2 …  Xi  Xi1 …
Initial state
(,Xi)
Evolution of the state
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
11
Sequential ASM
Software Technology Lab @ SFU
Formalization of the notion of sequential algorithm
Three postulates:
Sequential time
Abstract state
Bounded exploration
Syntax
We assume informally that any algorithm A can be given by a finite
text that explains the algorithm without presupposing any special
knowledge.
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
12
Distributed ASM
Software Technology Lab @ SFU
Asynchronous computation model (Gurevich, 1995)
Computational agents
Globally shared states
Concurrent moves
Semantic model resolves potential conflicts
according to the definition of partially ordered runs
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
13
Mastermind
Software Technology Lab @ SFU

Crime patterns in urban environments
P. L. Brantingham, U. Glässer, B. Kinney, K. Singh and M. Vajihollah. A
Computational Model for Simulating Spatial Aspects of Crime in Urban
Environments. In Proc. IEEE International Conference on Systems, Man and
Cybernetics, Oct. 2005
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
14
Crime is not random
Software Technology Lab @ SFU

Criminal events relate to people’s movement in the
course of everyday lifes
 Offenders commit offenses near places they spend
most of their time
 Victims are victimized near places where they spend
most of their time

Patterns/ rules that govern the working of a
social system

one composed of criminals, victims and targets
─ interacting with one another
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
15
Modeling and simulation
Software Technology Lab @ SFU
Motivation



Crime analysis and prevention
Integration of established theories
Reasoning about likely scenarios
Scope

Agents living in a virtual city

Commuting between home, work and recreation
Goals
Coherent and consistent semantic framework
 Computational models for discrete event simulation
 Integration and validation of patterns/ theories
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
16
Software Technology Lab @ SFU
Challenges and needs
``Computational
thinking’’

Common semantic framework
Abstract State Machines:


common core for linking
multi-disciplinary aspects
Semantic foundation
 Discrete mathematics
 Computational logic
Uwe Glässer
System
Dynamics
Environment
Planning
Approach

Multi-Agent
Systems
Criminology
Experimental
Validation
ASM
Navigation
AI/ALife
Knowledge
Represent.
Neural
Nets
Decision
Making
Learning
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
17
Mental Maps
Software Technology Lab @ SFU
“Every inhabitant of Amsterdam has an invisible map of
the city in his head. The way he moves about the city
and the choices made in this process are determined by
this mental map. Amsterdam Real Time attempts to
visualize these mental maps through examining the
mobile behavior of the city's users.”
 Amsterdam Real Time
Mental maps
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
18
Urban Environment(1)

Objective Environment
Software Technology Lab @ SFU


Subjective Environment



Subjective reality
Agent’s perception
Awareness Space


Physical reality
Part of perception
Geographic Environment
Objective
Environment
Perception
Awareness
Space
Subjective
Environment
Activity
Space
Activity Space


Uwe Glässer
Subset of awareness space
Frequently visited
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
19
Urban Environment(2)
Software Technology Lab @ SFU
Abstract mathematical data structure
Attributed Directed Graph
49 21’ 06”
123 15’ 04”
Max Speed
30 mi/h

Construction
Zone
Uwe Glässer
Traffic
density
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
20
Urban Environment(3)
Software Technology Lab @ SFU



Directed graph
H  (V,E)  topological aspects
Attributed directed graph
GGeoEnv  (H,)  attribution scheme (objective view)
Attributed directed graph with colored attributes
GEnv  (GGeoEnv ,)  subjective view (perception)
 Awareness space, activity space, crime occurrence space
{e  E density(a,e)  thresholdactivity}a
Goals: robustness, scalability, uniformity
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
21
Agent Architecture: BDI-based Model
Communication FROM Environment
Desires
Space Evolution Module
Profile
Target Selection Module
Cognition Rules
Agent Decision
Module
Cognition Rules
Intentions
Intentions
Deliberation
Working
Memory
Motivations
Intentions
Working
Memory
Perception
Action Rules
Means-End
Reasoning
Awareness
Space
Environment
Software Technology Lab @ SFU
Beliefs
Action Rules
Activity
Space
Communication TO Environment
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
22
Software Technology Lab @ SFU
Distributed ASM model
Computational
agents
Path planning
A
Master Agent
(PERSON agent)
S
e
D
B
C
SEM
TSM
ADM
agent
agent
agent
Space Evolution Module (SEM)


Agents move within their environment
Evolving spatial characteristics



Uwe Glässer
Awareness space
Activity space
Crime occurrence space
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
23
Software Technology Lab @ SFU
Simulation: Activity Space
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
24
Software Technology Lab @ SFU
Simulation: Activity Space
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
25
Software Technology Lab @ SFU
Simulation: Activity Space
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
26
Fitness of the model
Software Technology Lab @ SFU
Checking the validity

Role of modeling & simulation
 Descriptive rather than prescriptive
 Extracting behavior characteristics from response patterns
 Generating and testing hypothesis
 Identifying the system boundaries
 Understanding the effect of changes (causality)


Providing evidence for the validity of a model has a
different meaning than in prescriptive modeling
Compositional validation?
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
27
Simulation Model: Architecture
GIS Map
Software Technology Lab @ SFU
Text Files
Graphical
User
Interface
GIS2Graph
Map
(Graph)
Agent
Profiles
Visualization
Simulation
Engine
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
28
Safeguard
Software Technology Lab @ SFU

Aviation security
U. Glässer, S. Rastkar and M. Vajihollahi. Computational Modeling and
Experimental Validation of Aviation Security Procedures. In Proc. IEEE
International Conference on Intelligence and Security Informatics, volume
3975 of LNCS, pp. 420-431, Springer-Verlag, 2006.
Idle
secContrl
Ensured
Fals
e
Initialize-Screening
InProgress
secContrlPassed :=
True
secContrlPassed :=
False
Failed
Done
secContrlPassed :=
True
Perform-Screening
True
Uwe Glässer
Fals
e
Additional
ScreenReq
? True
Prepare-for-AdditionalScreening
Fals
e
Screening
Passed
True
Passed
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
29
Large area surveillance
Software Technology Lab @ SFU

Distributed information fusion and dynamic
resources management for decision support
Platforms
Swarm
CP140
MHP
Shared
informatio
n
CP140
MHP
UAV
UAV
UAV
Control
Stations
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
30
Summary

A novel approach to Computational Criminology
Software Technology Lab @ SFU

Modeling and simulation of crime patterns/ theories


Well defined and robust semantic framework



Tools for experimental research/ evidence based policy making
Multi-agent system modeling
ASM computation model
Results

Theoretical



Abstract behavior model of person agents (agent architecture)
Abstract data structure of the environment
Practical

Uwe Glässer
Mastermind model as platform for experimental development of
discrete event simulation models
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
31
Final remarks

Abstract state machines provide
Software Technology Lab @ SFU





an intuitive formalization of the notion of algorithm in a
fairly broad sense,
a practical instrument for analyzing and reasoning about
semantic properties of discrete dynamic systems,
abstract specifications that are executable in principle,
a corner stone in computer science education.
Interdisciplinary research @ SFU


ICURS: Computational Criminology (www.sfu.ca/icurs/)
IRMACS (www.irmacs.ca)
Uwe Glässer
Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007
32