Abstract
A new abstract model of interaction between agents and environments considered as objects of different types is introduced. Agents are represented by means of labelled transition systems considered up to bisimilarity. The equivalence of agents is characterised in terms of an algebra of behaviours which is a continuous algebra with approximation and two operations: nondeterministic choice and prefixing. Environments are introduced as agents supplied with an insertion function which takes the behaviour of an agent and the behaviour of an environment as arguments and returns the new behaviour of an environment. Arbitrary continuous functions can be used as insertion functions, and we use functions defined by means of rewriting logic as computable ones. The transformation of environment behaviours defined by the insertion function also defines a new type of agent equivalence – insertion equivalence. Two behaviours are insertion equivalent if they define the same transformation of an environment. The properties of this equivalence are studied. Three main types of insertion functions are used to develop interesting applications: one-step insertion, head insertion, and look-ahead insertion functions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Letichevsky, A.A., Kapitonova, J.V., Volkov, V.A., Chugajenko, A., Chomenko, V., Gilbert, D.R.: The development of interactive algorithms for a mathematical environment. In: Armando, A., Jebelean, T. (eds.) CALCULEMUS 1999, Systems for Integrated Computtion and Deduction. Electronic Notes in Theoretical Computer Sciences, pp. 33–50 (1999), http://www.elsevier.nl/locate/entcs
Abramsky, S.: A domain equation for bisimulation. Information and Computation 92(2), 161–218 (1991)
Abramsky, S.: Semantics of interaction. In: Kirchner, H. (ed.) CAAP 1996. LNCS, vol. 1059, p. 1. Springer, Heidelberg (1996)
Mason, I.A., Talkott, C.L.: Actor languages their syntax, semantics, translation, and equivalence. Theoretical Computer Science 220(2), 409–467 (1999)
Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Information and Control 60(1/3), 109–137 (1984)
Jacobs, B., Rutten, J.: A tutorial on (co)algebras and (co)induction. Bulletin of the EATCS 62, 222–259 (1997)
Park, D.M.R.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104. Springer, Heidelberg (1981)
Montanari, U., Gadducci, F.: The tile model. Technical Report TR-96-27, Department of Computer Science, University of Pisa (1996)
Gelernter, D., Zuck, L.: On What Linda is: Formal Description of Linda as a reactive system. In: Garlan, D., LeMetayer, D. (eds.) COORDINATION 1997. LNCS, vol. 1282, pp. 187–204. Springer, Heidelberg (1997)
Gilbert, D.R., Letichevsky, A.A.: A universal interpreter for nondeterministic concurrent programming languages. In: Gabbrielli, M. (ed.) Fifth Compulog network area meeting on language design and semantic analysis methods (September 1996)
Milne, G., Milner, R.: Concurrent processes and their syntax. J. Assoc. Comput. Mach. 26(2), 302 (1979)
Guessarian, I.: Algebraic semantics. LNCS, vol. 99. Springer, Heidelberg (1981)
Hoare, C.A.R.: Communicating Sequential Processes. Prentice Hall, Englewood Cliffs (1985)
Hoare, C.A.R., Jifeng, H.: Unifying Theories of Programming. Prentice Hall, Englewood Cliffs (1999)
Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science 96, 73–155 (1992)
Kapitonova, J.V., Letichevsky, A.A., Konozenko, S.V.: Computations in aps. Theoretical Computer Science 119, 145–171 (1993)
Letichevsky, A.A.: Algebras with approximation and recursive data structures. Kibernetika 5, 32–37 (1987)
Letichevsky, A.A., Gilbert, D.R.: Toward an implementation theory of nondeterministic concurrent languages. Technical Report 1996/09. ISSN 1364-4009, Department of Computer Science, City University (1996); Also presented at the Second workshop of the INTAS-93-1702 project Efficient Symbolic Computing St Petersburg, Russia (October 1996)
Letichevsky, A.A., Gilbert, D.R.: A general theory of action languages. Technical report, Department of Computer Science, City University, London, UK (August 1997)
Letichevsky, A.A., Gilbert, D.R.: Agents and environments. In: 1st International scientific and practical conference on programming, Proceedings 2-4 September, Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine (1998)
Letichevsky, A.A., Gilbert, D.R.: A general theory of action languages. Cybernetics and System Analysis 1, 16–36 (1998)
Lamport, L.: The temporal logic of actions. acm Transactions on Programming Languages and Systems 16(3), 872–923 (1994)
Barr, M.: Terminal coalgebras in well-founded set theory. Theoretical Computer Science 114(2), 299–315 (1993)
Milner, R.: Communication and Concurrency. Prentice Hall, Englewood Cliffs (1989)
Plotkin, G.: A structured approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Dept., Aarhus University (1981)
Saraswat, V.: Concurrent Constraint Programming. MIT Press, Cambridge (1993)
Valkevych, T., Gilbert, D.R., Letichevsky, A.A.: A generic workbench for modelling the behaviour of concurrent and probabilistic systems. In: Workshop on Tool Support for System Specification, Development and Verification, at TOOLS 1998, Malente, Germany, June 2–4 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Letichevsky, A., Gilbert, D. (2000). A Model for Interaction of Agents and Environments. In: Bert, D., Choppy, C., Mosses, P.D. (eds) Recent Trends in Algebraic Development Techniques. WADT 1999. Lecture Notes in Computer Science, vol 1827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44616-3_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-44616-3_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67898-4
Online ISBN: 978-3-540-44616-3
eBook Packages: Springer Book Archive