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117
Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
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Cited by 298 (31 self)
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In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (NonWellFounded sets, CSLI Leethre Notes, Vol. 14, center for the study of Languages and information, Stanford, 1988) on a theory of nonwellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages. Using the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras. Thus, the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to coalgebra, homomorphism of coalgebras, and bisimulation, respectively. In this paper, the latter are taken
The Linear TimeBranching Time Spectrum II  The semantics of sequential systems with silent moves
, 1993
"... ion Rule (KFAR) (Baeten, Bergstra & Klop [3]), expresses a global fairness assumption. It says that when possible a system will escape from any cycle of internal actions. Some form of KFAR is crucial for many protocal verifications with unreliable channels, and for that reason preorders and equivale ..."
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Cited by 290 (17 self)
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ion Rule (KFAR) (Baeten, Bergstra & Klop [3]), expresses a global fairness assumption. It says that when possible a system will escape from any cycle of internal actions. Some form of KFAR is crucial for many protocal verifications with unreliable channels, and for that reason preorders and equivalences that satisfy KFAR are of special interest. Must preorders and divergence sensitive ones cannot satisfy KFAR. In Bergstra, Klop & Olderog [7] it is shown that the combination of KFAR with failure semantics is inconsistent, but they formulate a weaker version of KFAR that is satisfied in failure maysemantics. Still the combination of KFAR \Gamma and the liveness requirement appears to require global testing, and is only satisfied in the semantics between contrasimulation (C) and stability respecting branching bisimulation (BB s ). These requirements would reduce the number of suitable preorders to 18. It is in general a good strategy to do your verifications using the finest preorde...
Probabilistic Simulations for Probabilistic Processes
, 1994
"... Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version o ..."
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Cited by 270 (18 self)
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Several probabilistic simulation relations for probabilistic systems are defined and evaluated according to two criteria: compositionality and preservation of "interesting" properties. Here, the interesting properties of a system are identified with those that are expressible in an untimed version of the Timed Probabilistic concurrent Computation Tree Logic (TPCTL) of Hansson. The definitions are made, and the evaluations carried out, in terms of a general labeled transition system model for concurrent probabilistic computation. The results cover weak simulations, which abstract from internal computation, as well as strong simulations, which do not.
Bisimulation for Labelled Markov Processes
 Information and Computation
, 1997
"... In this paper we introduce a new class of labelled transition systems  Labelled Markov Processes  and define bisimulation for them. ..."
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Cited by 139 (23 self)
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In this paper we introduce a new class of labelled transition systems  Labelled Markov Processes  and define bisimulation for them.
Priorities in process algebra
, 1999
"... This chapter surveys the semantic rami cations of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. The need for these enriched formalisms arises when one wishes to model system features such asinterrupts, prioritized ..."
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Cited by 103 (12 self)
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This chapter surveys the semantic rami cations of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. The need for these enriched formalisms arises when one wishes to model system features such asinterrupts, prioritized choice, orrealtime behavior. Approaches to priority in process algebras can be classi ed according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global preemption and static priorities and led to formalisms for modeling interrupts and aspects of realtime, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of preemption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the e cient encoding of realtime semantics. Technically, this chapter studies the di erent models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local preemption. In each case the operational semantics of CCS is modi ed appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for di erent processalgebraic settings are discussed.
The concurrency workbench: A semantics based tool for the verification of concurrent systems
 In Proceedings of the Workshop on Automatic Verification Methods for Finite State Machines
, 1991
"... Abstract The Concurrency Workbench is an automated tool for analyzing networks of finitestate processes expressed in Milner's Calculus of Communicating Systems. Its key feature is its breadth: a variety of different verification methods, including equivalence checking, preorder checking, and model ..."
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Cited by 102 (3 self)
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Abstract The Concurrency Workbench is an automated tool for analyzing networks of finitestate processes expressed in Milner's Calculus of Communicating Systems. Its key feature is its breadth: a variety of different verification methods, including equivalence checking, preorder checking, and model checking, are supported for several different process semantics. One experience from our work is that a large number of interesting verification methods can be formulated as combinations of a small number of primitive algorithms. The Workbench has been applied to the verification of communications protocols and mutual exclusion algorithms and has proven a valuable aid in teaching and research. 1 Introduction This paper describes the Concurrency Workbench [11, 12, 13], a tool that supports the automatic verification of finitestate processes. Such tools are practically motivated: the development of complex distributed computer systems requires sophisticated verification techniques to guarantee correctness, and the increase in detail rapidly becomes unmanageable without computer assistance. Finitestate systems, such as communications protocols and hardware, are particularly suitable for automated analysis because their finitary nature ensures the existence of decision procedures for a wide range of system properties.
Algebraic Reasoning for Probabilistic Concurrent Systems
 Proc. IFIP TC2 Working Conference on Programming Concepts and Methods
, 1990
"... We extend Milner's SCCS to obtain a calculus, PCCS, for reasoning about communicating probabilistic processes. In particular, the nondeterministic process summation operator of SCCS is replaced with a probabilistic one, in which the probability of behaving like a particular summand is given explicit ..."
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Cited by 94 (5 self)
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We extend Milner's SCCS to obtain a calculus, PCCS, for reasoning about communicating probabilistic processes. In particular, the nondeterministic process summation operator of SCCS is replaced with a probabilistic one, in which the probability of behaving like a particular summand is given explicitly. The operational semantics for PCCS is based on the notion of probabilistic derivation, and is given structurally as a set of inference rules. We then present an equational theory for PCCS based on probabilistic bisimulation, an extension of Milner's bisimulation proposed by Larsen and Skou. We provide the first axiomatization of probabilistic bisimulation, a subset of which is relatively complete for finitestate probabilistic processes. In the probabilistic case, a notion of processes with almost identical behavior (i.e., with probability 1 \Gamma ffl, for ffl sufficiently small) appears to be more useful in practice than a notion of equivalence, since the latter is often too restricti...
Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach
, 1998
"... . The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a ..."
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Cited by 75 (15 self)
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. The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation. Keywords. Bisimulation, probabilistic transition system, coalgebra, ultrametric space, Borel measure, final coalgebra. 1 Introduction For discrete probabilistic transition systems the notion of probabilistic bisimilarity of Larsen and Skou [LS91] is regarded as the basic process equivalence. The definition was given for reactive systems. However, Van Glabbeek, Smolka and Steffen s...
Weak Bisimulation for Fully Probabilistic Processes
, 1999
"... Bisimulations that abstract from internal computation have proven to be useful for verification of compositionally defined transition systems. In the literature of probabilistic extensions of such transition systems, similar bisimulations are rare. In this paper, we introduce weak and branching bisi ..."
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Cited by 57 (7 self)
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Bisimulations that abstract from internal computation have proven to be useful for verification of compositionally defined transition systems. In the literature of probabilistic extensions of such transition systems, similar bisimulations are rare. In this paper, we introduce weak and branching bisimulation for fully probabilistic systems, transition systems where nondeterministic branching is replaced by probabilistic branching. In contrast to the nondeterministic case, both relations coincide. We give an algorithm to decide weak (and branching) bisimulation with a time complexity cubic in the number of states of the fully probabilistic system. This meets the worst case complexity for deciding branching bisimulation in the nondeterministic case. In addition, the relation is shown to be a congruence with respect to the operators of PLSCCS , a lazy synchronous probabilistic variant of CCS. We illustrate that due to these properties, weak bisimulation provides all the crucial ingredients...
Process Algebra for Performance Evaluation
, 2000
"... This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resourcesharing systems  like largescale computers, clientserver architectur ..."
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Cited by 52 (13 self)
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This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resourcesharing systems  like largescale computers, clientserver architectures, networks  can accurately be described using such stochastic specification formalisms.