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Approximating Weak Bisimilarity of Basic Parallel Processes

2012
*
Electronic Proceedings in Theoretical Computer Science
*

This paper explores the well known

doi:10.4204/eptcs.89.8
fatcat:k7kvn74ngndc5c77a2kwkvqerm
*approximation*approach to decide*weak**bisimilarity**of**Basic**Parallel**Processes*. ... In particular, we show a lower bound*of*ω∗ω for the*approximants*which allow*weak*steps and a lower bound*of*ω + ω for the*approximants*that allow sequences*of*actions. ... We are grateful to the reviewers for their constructive feedback on earlier drafts*of*this document and thank Colin Stirling for many helpful discussions. ...##
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Weak bisimilarity between finite-state systems and BPA or normed BPP is decidable in polynomial time

2002
*
Theoretical Computer Science
*

We prove that

doi:10.1016/s0304-3975(01)00094-9
fatcat:mvqwcvb67fablpivp2waykjvea
*weak**bisimilarity*is decidable in polynomial time between ÿnite-state systems and several classes*of*inÿnite-state systems: context-free*processes*and normed*basic**parallel**processes*(normed ... To the best*of*our knowledge, these are the ÿrst polynomial algorithms for*weak**bisimilarity*problems involving inÿnite-state systems. ... We concentrate on the classes*of*inÿnite-state*processes*deÿnable by the syntax*of**basic**process*algebra (BPA) and normed*basic**parallel**processes*(BPP) systems. ...##
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Weak Bisimulation Approximants
[chapter]

2006
*
Lecture Notes in Computer Science
*

In this paper we consider a simple yet well-studied

doi:10.1007/11874683_24
fatcat:kls327zs5jgqhl6ibkyiaavy24
*process*algebra, the*Basic**Parallel**Processes*(BPP), and investigate for this class*of**processes*the minimal ordinal α such that ≈ = ≈α. ...*Bisimilarity*∼ and*weak**bisimilarity*≈ are canonical notions*of*equivalence between*processes*, which are defined co-inductively, but may be approached -and even reached -by their (transfinite) inductively-defined ... In this paper we consider the problem*of**weak**bisimilarity*for so-called*Basic**Parallel**Processes*(BPP), a simple yet well-studied model*of*concurrent*processes*. ...##
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Weak Bisimilarity with Infinite-State Systems Can Be Decided in Polynomial Time
[chapter]

1999
*
Lecture Notes in Computer Science
*

Semidecidability

doi:10.1007/3-540-48320-9_26
fatcat:lh2shkye35atjkxxbbb7vtagu4
*of**weak**bisimilarity*for BPP is due to [10] . ... To the best*of*our knowledge, these are the first polynomial algorithms for*weak**bisimilarity*with infinite-state systems. For*weak**bisimilarity*, much less is known. ... congruence w.r.t. sequencing, allows for unique decompositions*of*normed*processes*w.r.t. sequencing and*parallelism*, etc.). ...##
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Page 8174 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

Summary: “It is an open problem whether

*weak**bisimilarity*is decidable for*basic**process*algebra (BPA) and*basic**parallel*pro- cesses (BPP). ... Finally, we show how the technique for proving a co-NP lower bound for*weak**bisimilarity**of*BPA can be applied to strong*bisimilarity**of*BPP.” ...##
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A Polynomial-Time Algorithm for Deciding True Concurrency Equivalences of Basic Parallel Processes
[chapter]

2003
*
Lecture Notes in Computer Science
*

A polynomial-time algorithm is presented to decide distributed

doi:10.1007/978-3-540-45138-9_46
fatcat:eqav6xsjhrgjlnjc74xu2leumm
*bisimilarity**of**Basic**Parallel**Processes*. ... As a direct conclusion, several other noninterleaving semantic equivalences are also decidable in polynomial time for this class*of**process*, since they coincide with distributed*bisimilarity*. ... We study here the class*of**Basic**Parallel**Processes*[9] ( ÈÈ), an extension*of*recursively defined finite-state systems by*parallel*composition. ...##
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Decidability of Branching Bisimulation on Normed Commutative Context-Free Processes
[chapter]

2011
*
Lecture Notes in Computer Science
*

We investigate normed commutative context-free

doi:10.1007/978-3-642-23217-6_35
fatcat:5zxrdyzrkndfzfvwmzsznk5k3a
*processes*(*Basic**Parallel**Processes*). ... Keywords Branching bisimulation equivalence • Commutative context-free graphs • Equivalence checking •*Basic**parallel**processes*1 Introduction Bisimulation equivalence (*bisimilarity*) is a fundamental notion ... We investigate the class*of*commutative context-free*processes*, known also under name*Basic**Parallel**Processes*(BPP) [1] . ...##
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Decidability of Branching Bisimulation on Normed Commutative Context-Free Processes

2013
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Theory of Computing Systems
*

We investigate normed commutative context-free

doi:10.1007/s00224-013-9505-9
fatcat:yqqlxbfwg5awpfqs4alo4playq
*processes*(*Basic**Parallel**Processes*). ... Keywords Branching bisimulation equivalence • Commutative context-free graphs • Equivalence checking •*Basic**parallel**processes*1 Introduction Bisimulation equivalence (*bisimilarity*) is a fundamental notion ... We investigate the class*of*commutative context-free*processes*, known also under name*Basic**Parallel**Processes*(BPP) [1] . ...##
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Decidability of Weak Bisimilarity for a Subset of Basic Parallel Processes
[chapter]

2001
*
Lecture Notes in Computer Science
*

Decidability

doi:10.1007/3-540-45315-6_25
fatcat:pishtho2fjajfj23wdt5ldxgyu
*of**bisimilarity*was also shown for*Basic**Parallel*(BP)*processes*, a restricted subset*of*Petri nets, [4] . ... Normed*Basic**Parallel**processes*Ingredients*of**Basic**Parallel*(BP)*processes*are a finite set Γ = {X 1 , . . . , X n }*of*atoms, a finite set A = {a 1 , . . . , a k }*of*actions and a finite set T*of**basic*... By Fact 2*of*the previous section for some i, Proof*of*Lemma 2: Assume α ≈ γ. First also assume that α a =⇒ n α ′ and nf(α ′ ) ∈ E(α, a, n). Hence γ a =⇒ n γ ′ and nf(α ′ ) ≈ γ ′ . ...##
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Page 1317 of Mathematical Reviews Vol. , Issue 2003B
[page]

2003
*
Mathematical Reviews
*

)
Decidability

*of**weak**bisimilarity*for a subset*of**basic**parallel**processes*. ... In this paper we prove decidability*of**weak*bisimi- larity for a subset*of*normed BP*processes*for which inequivalence need not be finitely*approximable*. ...##
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Weak Bisimilarity Coalgebraically
[chapter]

2009
*
Lecture Notes in Computer Science
*

We argue that

doi:10.1007/978-3-642-03741-2_12
fatcat:jbtwovtaaffwrff2sxz7bhktpi
*weak**bisimilarity**of**processes*can be conveniently captured in a semantic domain by a combination*of*traces and coalgebraic finality, in such a way that important*process*algebra aspects ... We illustrate the usefulness*of*our approach by providing a fully-abstract denotational semantics for CCS under*weak**bisimilarity*. ... The strong*bisimilarity**of**processes*is a useful, but often too crude,*approximation**of**bisimilarity*, obtained by assuming the internal action τ observable. ...##
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Process Algebra and Markov Chains
[chapter]

2001
*
Lecture Notes in Computer Science
*

This paper surveys and relates the

doi:10.1007/3-540-44667-2_5
fatcat:lwdiknqzpfblzmzpr4mv6ila7a
*basic*concepts*of**process*algebra and the modelling*of*continuous time Markov chains. ... We then proceed to study the interrelation*of*reactive*processes*and Markov chains in this setting, and introduce the algebra*of*Interactive Markov Chains as an orthogonal extension*of*both*process*and ... stochastic*process*algebra over the past years. ...##
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Undecidability of bisimilarity by defender's forcing

2008
*
Journal of the ACM
*

The question

doi:10.1145/1326554.1326559
fatcat:ujkmzb2wrvagpgirtymhdemnui
*of*decidability*of**bisimilarity*for the more general class*of*so called Type -1 systems, which is equivalent to*weak**bisimilarity*on unrestricted ε-popping pushdown*processes*, was left open ... with*weak**bisimilarity**of**processes*generated by (unnormed) pushdown automata where the ε-transitions can only deterministically pop the stack. ... Our further results showed Σ 1 1 -completeness*of**weak**bisimilarity*on PA*processes*as well as Σ 1 1 -completeness*of**weak**bisimilarity*on PPDA*processes*(and Petri nets). ...##
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Highly Undecidable Questions for Process Algebras

2004
*
BRICS Report Series
*

We also show Pi^1_1-hardness

doi:10.7146/brics.v11i8.21833
fatcat:etmvtxf2gzbbtbcjddqxqa27um
*of**weak*omega-trace equivalence for the (sub)classes BPA (*basic**process*algebra) and BPP (*basic**parallel**processes*). ... We show Sigma^1_1-completeness*of**weak**bisimilarity*for PA (*process*algebra), and*of**weak*simulation preorder/equivalence for PDA (pushdown automata), PA and PN (Petri nets). ... PRS-hierarchy*Bisimilarity*is also known to be decidable for BPP (*basic**parallel**processes*); the only difference with BPA is that nonterminals are viewed as composed in*parallel*, i.e., each can be rewritten ...##
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Bisimulation Trees and the Decidability of Weak Bisimulations

1997
*
Electronical Notes in Theoretical Computer Science
*

We d e v elop \bisimulation trees" as a means to prove decidability o f w eak bisimulation for restricted classes

doi:10.1016/s1571-0661(05)80674-7
fatcat:46jmx6srozd75jzxon74m2yrhe
*of*BPP and BPA. ... Conclusion We already stated the conjecture that eventually it will be shown that*weak*(and branching) bisimulation is decidable. ... The work that was needed to prove the result for the very restricted case*of*totally normed BPA (either here or in 11]) is discouraging. ...
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