A Comparison of DEVS and Semantic Composability Theory

1
A Comparison of DEVS and Semantic Composability
Theory

• Eric W. Weisel, Ph.D.WernerAnderson, Inc.6596
  Main StreetGloucester VA 23061eweisel_at_wernerande
  rson.com 804-694-3173
• Mikel D. Petty, Ph.D. and Roland R. Mielke,
  Ph.D.Virginia Modeling, Analysis and Simulation
  CenterOld Dominion UniversityNorfolk VA
  23529mpetty_at_vmasc.odu.edu 757-686-6210
• rmielke_at_odu.edu 757-686-6211

2

• This research is sponsored by the Defense
  Modeling and Simulation Office. That support is
  gratefully acknowledged.

3
Purpose

• Because DEVS and semantic composability theory
  appear to have certain topics in common, notably
  the composition of models, the question of their
  relationship has arisen
• Address the question directly by comparing DEVS
  and Semantic Composability Theory

4
Outline

• Basis for comparison
• Semantic Composability Theory (previous
  presentation)
• DEVS
• Informal comparison of formalisms
• DTSS, computation, and power

5
DEVS and related formalisms

• Three basic formalisms for system specification
• Discrete Event System Specification (DEVS)
• Discrete Time System Specification (DTSS)
• Differential Equation System Specification (DESS)

Arrows represent sub-class relationships
6
DEVS
7
DTSS
8
Informal comparison of formalisms

• Similarities
• One formalism can be written in terms of the
  other
• Differences
• Computability

9
Informal comparison of formalisms
10
Informal comparison of formalisms
11
Relationship of DEVS to computation

• Composability theory takes as its domain all
  computable functions
• Includes all models and simulations that run on a
  computer
• The set of computable functions are all those
  functions computable on a digital computer or on
  any abstract model of computation, such as a
  Turing machine this set encompasses all that is
  computable and defines computation
• Therefore, relating DEVS to computation will
  allow a comparison of the computation power of
  the two theories

12
Relationship of DEVS to computation

• We will work primarily with DTSS
• Note that a standard DTSS specification could be
  uncomputable in at least two ways.
• If any of X, Y, or Q are uncountably infinite
  sets, such as the real numbers, the DTSS
  specification is not computable.
• If the transition function is not computable,
  then the DTSS specification is not computable.

An uncomputable specification cannot be executed
as written on a simulator.
13
C-DTSS

• We therefore define a version of DTSS, called
  Computable-DTSS (C-DTSS)
• C-DTSS is simply DTSS with restrictions to ensure
  that its processing is computable.
• Because C-DTSS is a restricted form of DTSS, all
  C-DTSS specifications are DTSS specifications.

14
C-DTSS
15
Comparison of C-DTSS to DTSS
16
Theorem

• The set of computable functions and C-DTSS
  specifications are equivalent in computational
  power.
• Proof. To prove the theorem, it suffices to
  show
• given any computable function, there is a C-DTSS
  specification that performs the same computation
  and
• given any C-DTSS execution, there is a computable
  function that performs the same computation.

17
Theorem

• (1) Let fC be an arbitrary computable function.
  Define C-DTSS specification C (?, ?, N, fC, ?
  ? ?, 1). Then C performs the same computation
  as fC.
• (2) Let q1, q2, , qn be an arbitrary execution
  of a C-DTSS specification C (?,?, N, ?, ?, c).
  By definition of C-DTSS, each transition qi ?
  qi1 for 1 ? i ? n 1 is computable by
  computable function ?. Then any state in the
  execution qj is computable as ?(?( ?(q1) )),
  with j 1 executions of ? note that j may be n,
  i.e., the final state of the execution. This
  computation is a simple composition of a
  computable function. The set of computable
  functions is closed under composition, i.e., any
  composition of computable functions is itself a
  computable function. Therefore, there is a
  computable function that computes any state in
  the C-DTSS execution.

18
Corollary

• When considering system specifications to be
  executed on a simulator that is a computer, all
  of the DEVS formalisms (DTSS, DEVS, DESS) and
  their various extensions and combinations are
  equivalent in computational power.
• Proof. C-DTSS specifications are DTSS
  specifications, so DTSS and the other DEVS
  formalisms are at least as powerful as C-DTSS.
  But by the theorem presented in the previous
  slides C-DTSS and computable functions are
  equivalent in computational power both can
  compute anything computable. Thus, when
  restricted to computers as simulators, DTSS,
  DEVS, DESS, and their variants and extensions
  cannot be more powerful than C-DTSS. Therefore,
  under that restriction, the formalisms are all
  equivalent.

19
Results
Composability theory and C-DTSS are both
sufficiently powerful to express all simulations
that can run on a computer
20
Results

• Composability theory and C-DTSS (and thus DTSS,
  DEVS, etc.) are both sufficiently powerful to
  express all simulations that can run on a
  computer
• The question of which theory to use for a
  specific application will thus depend on
  ease-of-use with respect to that application.
• We believe that for specifying models DEVS may
  often be preferable because of its various
  modeling-specific features. However, it is
  possible to write correct but uncomputable DEVS
  specifications.
• For that reason we believe that composability
  theory is appropriate for studying simulation and
  composability from a theoretical point of view.

21
References

• M. D. Petty and E. W. Weisel, A Composability
  Lexicon, Proceedings of the Spring 2003
  Simulation Interoperability Workshop, Orlando FL,
  March 30-April 4 2003, pp. 181-187.
• E. W. Weisel, M. D. Petty, and R. M. Mielke, A
  Survey of Engineering Approaches to
  Composability, Proceedings of the Spring 2004
  Simulation Interoperability Workshop, Arlington
  VA, April 18-23 2004.
• S. Porcarelli, M. Castaldi, F. Di Giandomenico,
  A. Bondavalli, and P. Inverardi, A Framework for
  Reconfiguration-Based Fault-Tolerance in
  Distributed Systems, in R. de Lemos, C. Gacek,
  and A. Romanovsky (Eds.), Architecting Dependable
  Systems, Volume 2, Lecture Notes in Computer
  Science, Springer-Verlag, New York NY.
• S. Waziruddin, D. C. Brogan, and P. F. Reynolds,
  The Process for Coercing Simulations,
  Proceedings of the Fall 2003 Simulation
  Interoperability Workshop, Orlando FL, September
  14-19 2003.
• R. R. Mielke and M. A. Phillips, Development and
  Application of an Academic Battle Lab,
  Proceedings of the 2003 Interservice/Industry
  Training, Simulation and Education Conference,
  Orlando FL, December 1-4 2003, pp. 1371-1380.
• P. K. Davis and R. H. Anderson, Improving the
  Composability of Department of Defense Models and
  Simulations, RAND National Defense Research
  Institute, Santa Monica CA, 2004.

• P. K. Davis and R. H. Anderson, Improving the
  Composability of Department of Defense Models and
  Simulations, Journal of Defense Modeling and
  Simulation, Vol. 1, No. 1, January 2004, pp.
  5-17.
• M. D. Petty and E. W. Weisel, A Formal Basis for
  a Theory of Semantic Composability, Proceedings
  of the Spring 2003 Simulation Interoperability
  Workshop, Orlando FL, March 30-April 4 2003, pp.
  416-423.
• M. D. Petty, E. W. Weisel and R. R. Mielke, A
  Formal Approach to Composability, Proceedings of
  the 2003 Interservice/Industry Training,
  Simulation and Education Conference, Orlando FL,
  December 1-4 2003, pp. 1763-1772.
• E. W. Weisel, R. R. Mielke, and M. D. Petty,
  Validity of Models and Classes of Models in
  Semantic Composability, Proceedings of the Fall
  2003 Simulation Interoperability Workshop,
  Orlando FL, September 14-19 2003, pages 526-536.
• M. D. Petty, E. W. Weisel, and R. R. Mielke,
  Computational Complexity of Selecting Models for
  Composition, Proceedings of the Fall 2003
  Simulation Interoperability Workshop, Orlando FL,
  September 14-19 2003, pages 517-525.
• E. H. Page and J. M. Opper, Observations on the
  Complexity of Composable Simulation, Proceedings
  of the 1999 Winter Simulation Conference, Phoenix
  AZ, December 5-8 1999, pp. 553-560.
• M. D. Petty, Simple Composition Suffices to
  Assemble Any Composite Model, Proceedings of the
  Spring 2004 Simulation Interoperability Workshop,
  Arlington VA, April 18-23 2004, pp. 299-307.

22
References

• B. P. Zeigler, H. Praehofer, and T. G. Kim,
  Theory of Modeling and Simulation, Second
  Edition, Academic Press, San Diego CA, 2000.
• S. Kasputis, I. Osvalt, R. McKay, and S. Barber,
  Semantic Descriptors of Models and Simulations,
  Proceedings of the Spring 2004 Simulation
  Interoperability Workshop, Arlington VA, April
  18-23 2004.
• Simulation Interoperability Standards
  Organization, Base Object Model (BOM) Template
  Specification Volume I Interface BOM,
  SISO-STD-003.1-TRIAL-USE-V0.9, July 23 2004,
  On-line at http//www.boms.info/spec/BOM_VolI_v0_9
  _trialuse.pdf.
• P. D. Mosses, Denotational semantics, in J. van
  Leeuwen (Ed.), Handbook of Theoretical Computer
  Science, Vol. B - Formal Models and Semantics,
  Elsevier, Amsterdam The Netherlands 1990,
  pp. 573-631.
• W. Wymore, Model-Based Systems Engineering, CRC
  Press, Boca Raton FL, 1993.
• S. Y. Harmon, Interoperability between
  Distributed Simulations I Interacting Models of
  Physical Processes, Proceedings of the 15th
  Workshop on the Interoperability of Distributed
  Interactive Simulation, Orlando FL, September
  16-20 1996.
• M. Roggenbach and M. Majster-Cederbaum, Towards
  a Unified View of Bisimulation A Comparative
  Study, Theoretical Computer Science, Vol. 238,
  pp. 81-130, 2000.
• A. Borälv and G. Stålmarck, Formal Verification
  in Railways, in M. G. Hinchey and J. P. Bowen
  (Eds.), Industrial-Strength Formal Methods in
  Practice, Springer-Verlag, London, pp. 329-350,
  1999.

• N. Halbwachs, P. Caspi, P. Raymond, and D.
  Pilaud, The synchronous data flow programming
  language LUSTRE, Proceedings of the IEEE, Vol.
  79, Iss. 9, pp. 1305-1320, September 1991.
• M. D. Petty, E. W. Weisel, and R. R. Mielke,
  Composability Theory Overview and Update,
  Proceedings of the Spring 2005 Simulation
  Interoperability Workshop, April 3-8 2005, San
  Diego CA.
• J. B. Collins and D. Clark, Towards an Ontology
  of Physics, Proceedings of the 2004 European
  Simulation Interoperability Workshop, Edinburgh
  Scotland, June 28-July 1 2004.
• J. B. Collins, Standardizing an Ontology of
  Physics for Modeling and Simulation, Proceedings
  of the Fall 2004 Simulation Interoperability
  Workshop, September 19-24 2004, Orlando FL.
• M. D. Davis, R. Sigal, and E. J. Weyuker,
  Computability, Complexity, and Languages,
  Fundamentals of Theoretical Computer Science,
  Second Edition, Morgan Kaufmann, San Diego CA,
  1994.

23
Questions?