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27
Axiomatizing Flat Iteration
, 1997
"... ion Rule [4]. Like FIR, FFIR expresses that modulo weak (or delay) congruence a process remains the same if ø loops are added (or deleted) in (or from) its proper derivatives. The law FT1 has the same function in branching (or j)bisimulation semantics, but has to be formulated more carefully becau ..."
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ion Rule [4]. Like FIR, FFIR expresses that modulo weak (or delay) congruence a process remains the same if ø loops are added (or deleted) in (or from) its proper derivatives. The law FT1 has the same function in branching (or j)bisimulation semantics, but has to be formulated more carefully because T2 is not valid there. Note that FT1 can be reformulated as ff:(s+ø) x = ff:s x. The laws FT2 and FT3 are straightforward generalizations of the laws PB2 and PT3 of [2]. The remaining law PT2 of [2] is (by the forthcoming completeness theorem for $ c d ) derivable from the ones given here. Note that even over a finite alphabet A there exist infinitely many sumforms. Hence the axiomatizations as given here are infinite. However, for each axiom scheme only the instantiations are needed in which the sumforms have the form P n i=1 ff i in which all the ff i 's are different. With this modification each of the axiom systems E @ (@ 2 fs; b; j; d; wg) is finite if so is the set of acti...
A complete axiomatisation of branching bisimulation for process algebras with alternative quantification over data
, 1998
"... ..."
Minimization of Large State Spaces using Symbolic Branching Bisimulation
 In Proc. of DDECS’06
, 2006
"... Abstract: Bisimulations in general are a powerful concept to minimize large finite state systems regarding some welldefined observational behavior. In contrast to strong bisimulation, for branching bisimulation there are only tools available that work on an explicit state space representation. In t ..."
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Abstract: Bisimulations in general are a powerful concept to minimize large finite state systems regarding some welldefined observational behavior. In contrast to strong bisimulation, for branching bisimulation there are only tools available that work on an explicit state space representation. In this work we present for the first time a symbolic approach for branching bisimulation that uses BDDs as basic data structure and that is based on the concept of signature refinement. First experimental results for problem instances derived from process algebraic system descriptions show the feasibility and the robustness of our approach. 1
Is timed branching bisimilarity an equivalence indeed
 In Formal Modeling and Analysis of Timed Systems, Third International Conference, FORMATS 2005
, 2005
"... Abstract. We show that timed branching bisimilarity as defined by van der Zwaag [14] and Baeten & Middelburg [2] is not an equivalence relation, in case of a dense time domain. We propose an adaptation based on van der Zwaag’s definition, and prove that the resulting timed branching bisimilarity is ..."
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Abstract. We show that timed branching bisimilarity as defined by van der Zwaag [14] and Baeten & Middelburg [2] is not an equivalence relation, in case of a dense time domain. We propose an adaptation based on van der Zwaag’s definition, and prove that the resulting timed branching bisimilarity is an equivalence indeed. Furthermore, we prove that in case of a discrete time domain, van der Zwaag’s definition and our adaptation coincide. 1
Equational reasoning on ad hoc networks
 In Proceedings of the Third International Conference on Fundamentals of Software Engineering (FSEN
, 2009
"... Abstract. We provide an equational theory for Restricted Broadcast Process Theory to reason about ad hoc networks. We exploit an extended algebra called Computed Network Theory to axiomatize restricted broadcast. It allows one to define an ad hoc network with respect to the underlying topologies. We ..."
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Abstract. We provide an equational theory for Restricted Broadcast Process Theory to reason about ad hoc networks. We exploit an extended algebra called Computed Network Theory to axiomatize restricted broadcast. It allows one to define an ad hoc network with respect to the underlying topologies. We give a sound and complete axiomatization for the recursionfree part of the term algebra CNT, modulo what we call rooted branching computed network bisimilarity. 1
Normed Processes, Unique Decomposition, and Complexity of Bisimulation Equivalences
"... We propose a decision procedure for a general class of normed commutative process rewrite systems and their induced bisimulation equivalences. Our technique is inspired by the polynomialtime algorithm for strong bisimilarity on normed Basic Parallel Processes (BPP), developed by Hirshfeld, Jerrum a ..."
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We propose a decision procedure for a general class of normed commutative process rewrite systems and their induced bisimulation equivalences. Our technique is inspired by the polynomialtime algorithm for strong bisimilarity on normed Basic Parallel Processes (BPP), developed by Hirshfeld, Jerrum and Moller. As part of our framework we present a generic unique decomposition result, which we obtain by building on a characterization by Luttik and van Oostrom. We apply our general technique to derive polynomialtime algorithms for strong bisimilarity on normed BPP with communication and for distributed bisimilarity on all BPP with communication. Moreover, our technique yields a PSPACE upper bound for weak and branching bisimilarity on totally normed BPP.
Cones and foci: A mechanical framework for protocol verification
"... Abstract We define a cones and foci proof method, which rephrases the question whether two system specifications are branching bisimilar in terms of proof obligations on relations between data objects. Compared to the original cones and foci method from Groote and Springintveld, our method is more g ..."
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Abstract We define a cones and foci proof method, which rephrases the question whether two system specifications are branching bisimilar in terms of proof obligations on relations between data objects. Compared to the original cones and foci method from Groote and Springintveld, our method is more generally applicable, because it does not require a preprocessing step to eliminate τloops. We prove soundness of our approach and present a set of rules to prove the reachability of focus points. Our method has been formalized and proved correct using PVS. Thus we have established a framework for mechanical protocol verification. We apply this framework to the Concurrent Alternating Bit Protocol.
Operational semantics for Petri net components
, 2007
"... We propose a calculus for marked labelled nets (components), with places and transitions as atoms and merge, addition, fusion and relabelling as operators. The operators are defined using graphbased transformations; each net can be represented by a term. Next, we define both a step semantics for ne ..."
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We propose a calculus for marked labelled nets (components), with places and transitions as atoms and merge, addition, fusion and relabelling as operators. The operators are defined using graphbased transformations; each net can be represented by a term. Next, we define both a step semantics for nets and a Plotkinstyle SOS semantics for net terms and show their equivalence. In the semantics, both stateoriented and eventoriented properties of components can be expressed. We give a few rules for reducing components to smaller equivalent ones.
M.: Action abstraction in timed process algebra: The case for an untimed silent step
, 2006
"... Abstract. This paper discusses action abstraction in timed process algebras. It is observed that the leading approaches to action abstraction in timed process algebra all maintain the timing of actions, even if these actions are abstracted from. This paper presents a novel approach to action abstrac ..."
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Abstract. This paper discusses action abstraction in timed process algebras. It is observed that the leading approaches to action abstraction in timed process algebra all maintain the timing of actions, even if these actions are abstracted from. This paper presents a novel approach to action abstraction in timed process algebras. Characteristic for this approach is that in abstracting from an action, also its timing is abstracted from. We define an abstraction operator and a timed variant of rooted branching bisimilarity and establish that this notion is an equivalence relation and a congruence. 1
Complete Axiomatisations of Weak, Delay and ηBisimulation for Process Algebras with Alternative Quantification over Data
, 1999
"... Groote and Luttik (1998a) proved that the extension of the theory pCRL with the axioms for branching bisimulation of Van Glabbeek and Weijland (1996) yields a ground complete axiomatisation of branching bisimulation algebras with data, and conditionals and alternative quantification over these, prov ..."
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Groote and Luttik (1998a) proved that the extension of the theory pCRL with the axioms for branching bisimulation of Van Glabbeek and Weijland (1996) yields a ground complete axiomatisation of branching bisimulation algebras with data, and conditionals and alternative quantification over these, provided that the data part has builtin equality and builtin Skolem functions. In this paper we shall use this result to obtain ground complete axiomatisations of #bisimulation algebras, delay bisimulation algebras and weak bisimulation algebras with data, conditionals and alternative quantification over data, under the same proviso as before. 1991 Mathematics Subject Classification: 03G25; 08A70; 68Q65; 68Q70 1991 Computing Reviews Classification System: D.1.3; F.1.1; F.4.1 Keywords and Phrases: Generalised Algebra, Process Algebra, Algebraic Specification, Alternative Quantification, Input Prefixing, Weak Bisimulation, Silent Step, Abstraction. Note: Research supported by the Netherlands...