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Forward and Backward Simulations  Part II: TimingBased Systems
 Information and Computation
, 1995
"... A general automaton model for timingbased systems is presented and is used as the context for developing a variety of simulation proof techniques for such systems. These techniques include (1) refinements, (2) forward and backward simulations, (3) hybrid forwardbackward and backwardforward sim ..."
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Cited by 85 (29 self)
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A general automaton model for timingbased systems is presented and is used as the context for developing a variety of simulation proof techniques for such systems. These techniques include (1) refinements, (2) forward and backward simulations, (3) hybrid forwardbackward and backwardforward simulations, and (4) history and prophecy relations. Relationships between the different types of simulations, as well as soundness and completeness results, are stated and proved. These results are (with one exception) analogous to the results for untimed systems in Part I of this paper. In fact, many of the results for the timed case are obtained as consequences of the analogous results for the untimed case.
The cones and foci proof technique for timed transition systems
 Information Processing Letters
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A complete axiomatisation of branching bisimulation for process algebras with alternative quantification over data
, 1998
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An Axiomatization for Regular Processes in Timed Branching Bisimulation
 Fundamenta Informaticae
, 1998
"... ion The previous section treated BPA ffir with recursion modulo timed strong bisimulation. In this section the alphabet is extended with a special constant ø , to obtain BPA ffiø r with recursion, and process terms are considered modulo rooted timed branching bisimulation. In the sequel, a and ff w ..."
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Cited by 5 (0 self)
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ion The previous section treated BPA ffir with recursion modulo timed strong bisimulation. In this section the alphabet is extended with a special constant ø , to obtain BPA ffiø r with recursion, and process terms are considered modulo rooted timed branching bisimulation. In the sequel, a and ff will represent elements from A [ føg and A [ fffi; øg, respectively. 3.1 Time Shift In order to define timed branching bisimulation, the syntax is extended with the time shift operator (r)p, which takes a rational number r and a process term p. The process term (r)p denotes the behaviour of p that is shifted r units in time. Its ultimate delay is defined by U((r)p) = maxfU(p) + r; 0g The transition rules and axioms for the time shift are given in Table 4. Using axioms TS14, this operator can be eliminated from all process terms. 3.2 Timed Branching Bisimulation The operational semantics consists of the transition rules in Table 1 and Table 2 and Table 4. The definition of timed strong...
personal communication
, 1993
"... Abstract. We show that timed branching bisimilarity as defined by Van der Zwaag [17] and Baeten and 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 i ..."
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Abstract. We show that timed branching bisimilarity as defined by Van der Zwaag [17] and Baeten and 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. Finally, we prove that a rooted version of timed branching bisimilarity is a congruence over a basic timed process algebra containing parallelism, successful termination and deadlock. 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 ..."
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Cited by 3 (2 self)
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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
Formal verification of timed systems using cones and foci
 PROCEEDINGS OF THE 6TH WORKSHOP ON REALTIME SYSTEMS (ARTS’04
, 1998
"... The cones and foci verification method from Groote and Springintveld [9] was extended to timed systems by van der Zwaag [17]. We present an extension of this cones and foci method for timed systems, which can cope with infinite τsequences. We prove soundness of our approach and give small verifica ..."
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Cited by 1 (1 self)
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The cones and foci verification method from Groote and Springintveld [9] was extended to timed systems by van der Zwaag [17]. We present an extension of this cones and foci method for timed systems, which can cope with infinite τsequences. We prove soundness of our approach and give small verification examples.
A Complete Axiomatisation of Branching Bisimulation for Process Algebras With Alternative Quantification Over Data
, 1998
"... We define a class of process algebras with silent step and a generalised operation P that allows explicit treatment of alternative quantification over data, and we investigate the specific subclass formed by the algebras of finite processes modulo rooted branching bisimulation. We give a ground co ..."
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We define a class of process algebras with silent step and a generalised operation P that allows explicit treatment of alternative quantification over data, and we investigate the specific subclass formed by the algebras of finite processes modulo rooted branching bisimulation. We give a ground complete axiomatisation for those branching bisimulation algebras of which the data part has builtin equality and Skolem functions. 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, Strong Bisimulation, Branching Bisimulation, Silent Step, Abstraction. Note: Research supported by the Netherlands Organization for Scientific Research (NWO) under contract SION 61233008. Work carried out under project SEN 2.1 Process Specification and Analysis. 1. Introduction In Groote and Lutti...