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15
Equational axioms for probabilistic bisimilarity
 IN PROCEEDINGS OF 9TH AMAST, LECTURE NOTES IN COMPUTER SCIENCE
, 2002
"... This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finitestate agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571595). The axiomatization is obtained by extending ..."
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Cited by 18 (0 self)
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This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finitestate agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571595). The axiomatization is obtained by extending the general axioms of iteration theories (or iteration algebras), which characterize the equational properties of the fixed point operator on (#)continuous or monotonic functions, with three axiom schemas that express laws that are specific to probabilistic bisimilarity.
Nested Semantics over Finite Trees are Equationally Hard
, 2003
"... This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied ..."
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Cited by 15 (11 self)
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This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied in this paper, the collection of sound, closed (in)equations over a singleton action set is not finitely based.
The MaxPlus Algebra of the Natural Numbers has no Finite Equational Basis
 SCI
, 1999
"... This paper shows that the collection of identities which hold in the algebra N of the natural numbers with constant zero, and binary operations of sum and maximum is not finitely based. Moreover, it is proven that, for every n, the equations in at most n variables that hold in N do not form an eq ..."
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Cited by 10 (6 self)
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This paper shows that the collection of identities which hold in the algebra N of the natural numbers with constant zero, and binary operations of sum and maximum is not finitely based. Moreover, it is proven that, for every n, the equations in at most n variables that hold in N do not form an equational basis. As a stepping stone in the proof of these facts, several results of independent interest are obtained. In particular, explicit descriptions of the free algebras in the variety generated by N are offered. Such descriptions are based upon a geometric characterization of the equations that hold in N, which also yields that the equational theory of N is decidable in exponential time.
2Nested Simulation is not Finitely Equationally Axiomatizable
 IN
, 2000
"... 2nested simulation was introduced by Groote and Vaandrager [10] as the coarsest equivalence included in completed trace equivalence for which the tyft/tyxt format is a congruence format. In the linear timebranching time spectrum of van Glabbeek [8], 2nested simulation is one of the few equivalenc ..."
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Cited by 9 (5 self)
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2nested simulation was introduced by Groote and Vaandrager [10] as the coarsest equivalence included in completed trace equivalence for which the tyft/tyxt format is a congruence format. In the linear timebranching time spectrum of van Glabbeek [8], 2nested simulation is one of the few equivalences for which no finite equational axiomatization is presented. In this paper we prove that such an axiomatization does not exist for 2nested simulation.
Some of My Favourite Results in Classic Process Algebra
 In Bulletin of the EATCS
, 2003
"... this paper has generated a veritable industry of results on the metatheory of SOS and process algebras. (See [10] for a mention of some of these achievements and pointers to the original literature.) The proof techniques used in these results were extremely ingenious, and have paved the way to many ..."
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Cited by 9 (3 self)
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this paper has generated a veritable industry of results on the metatheory of SOS and process algebras. (See [10] for a mention of some of these achievements and pointers to the original literature.) The proof techniques used in these results were extremely ingenious, and have paved the way to many similar developments. Again, the role played by the modal characterizations of behavioural equivalences in the proof of the characterizations of the largest congruences is remarkable
Equational Theories of Tropical Semirings
 THEORETICAL COMPUTER SCIENCE
, 2001
"... This paper studies the equational theory of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime ..."
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Cited by 4 (0 self)
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This paper studies the equational theory of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime examples of such structures are the (max, +) semiring and the tropical semiring. It is shown that none of the exotic semirings commonly considered in the literature has a finite basis for its equations, and that similar results hold for the commutative idempotent weak semirings that underlie them. For each of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results.
The Netherlands
 In Martin Jaenicke and Helmut Weidner (eds.), National Environmental Policies
, 1997
"... This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied i ..."
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This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied in this paper, the collection of sound, closed (in)equations over a singleton action set is not finitely based. Key words: Concurrency, process algebra, BCCSP, nested simulation, possible futures, nested trace semantics, equational logic, complete axiomatizations, nonfinitely based algebras, HennessyMilner logic
A Cook's Tour of Equational Axiomatizations for Prefix Iteration
 IN PROCEEDINGS OF THE 1ST CONFERENCE ON FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES (FOSSACS’98
, 1998
"... Prefix iteration is a variation on the original binary version of the Kleene star operation PQ, obtained by restricting the first argument to be an atomic action, and yields simple iterative behaviours that can be equationally characterized by means of finite collections of axioms. In this paper, we ..."
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Prefix iteration is a variation on the original binary version of the Kleene star operation PQ, obtained by restricting the first argument to be an atomic action, and yields simple iterative behaviours that can be equationally characterized by means of finite collections of axioms. In this paper, we present axiomatic characterizations for a significant fragment of the notions of equivalence and preorder in van Glabbeek's lineartime/branchingtime spectrum over Milner's basic CCS extended with prefix iteration. More precisely, we consider ready simulation, simulation, readiness, trace and language semantics, and provide complete (in)equational axiomatizations for each of these notions over BCCS with prefix iteration. All of the axiom systems we present are finite, if so is the set of atomic actions under consideration.
Abstract Simple equations on binary factorial languages ⋆
"... We consider equations on the monoid of factorial languages on the binary alphabet. We use the notion of a canonical decomposition of a factorial language and previous results by Avgustinovich and the author to solve several simple equations on binary factorial languages including X n = Y n, the comm ..."
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We consider equations on the monoid of factorial languages on the binary alphabet. We use the notion of a canonical decomposition of a factorial language and previous results by Avgustinovich and the author to solve several simple equations on binary factorial languages including X n = Y n, the commutation equation XY = Y X and the conjugacy equation XZ = ZY. At the end of the paper we discuss the difficulties hindering to reduce equations on factorial languages to equations on words and to enlarge the alphabet considered.