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Undecidability Results for Bisimilarity on Prefix Rewrite Systems [chapter]

Petr Jančar, Jiří Srba
2006 Lecture Notes in Computer Science  
We answer an open question related to bisimilarity checking on labelled transition systems generated by prefix rewrite rules on words.  ...  The question of decidability of bisimilarity for a more general class of so called Type -1 systems (generated by prefix rewrite rules of the form R a −→ w where R is a regular language) was left open;  ...  The authors thank to Géraud Sénizergues for a motivating discussion (at University of Stuttgart) and acknowledge a support from the Alexander von Humboldt Foundation.  ... 
doi:10.1007/11690634_19 fatcat:pmekz42wwjdbrdz7hlaqh7bd3q

Undecidability Results for Bisimilarity on Prefix Rewrite Systems

Petr Jancar, Jirí Srba
2006 BRICS Report Series  
We answer an open question related to bisimilarity checking on labelled transition systems generated by prefix rewrite rules on words.  ...  The question of decidability of bisimilarity for a more general class of so called Type -1 systems (generated by prefix rewrite rules of the form R ---> w where R is a regular language) was left open;  ...  The authors thank to Géraud Sénizergues for a motivating discussion (at University of Stuttgart) and acknowledge a support from the Alexander von Humboldt Foundation.  ... 
doi:10.7146/brics.v13i7.21913 fatcat:xdsvbn4evvasxf75fjntobpydm

Undecidability of bisimilarity by defender's forcing

Petr Jančar, Jivří Srba
2008 Journal of the ACM  
Firstly, we classify several versions of the undecidable problems for prefix rewrite systems (or pushdown automata) as Π 0 1 -complete or Σ 1 1 -complete.  ...  Here we answer the question negatively, i.e., we show the undecidability of bisimilarity on Type -1 systems, even in the normed case.  ...  Section 5 contains the results for prefix-rewrite systems and pushdown automata, Section 6 then deals with PA processes, and Section 7 with PPDA (and Petri nets). Section 8 summarizes the results.  ... 
doi:10.1145/1326554.1326559 fatcat:ujkmzb2wrvagpgirtymhdemnui

Refining the Undecidability Border of Weak Bisimilarity

Mojmír Křetínský, Vojtěch Řehák, Jan Strejček
2006 Electronical Notes in Theoretical Computer Science  
Adding a finite-state control unit to the PRS rewriting mechanism results in so-called state-extended PRS (sePRS) classes, see for example [8] .  ...  State of the art: Regarding sequential systems, i.e. those without parallel composition, the weak bisimilarity problem is undecidable for PDA even for the normed case [19] .  ...  We would like to thank Jiří Srba for valuable suggestions and comments.  ... 
doi:10.1016/j.entcs.2005.11.014 fatcat:acux3qkpmnc2vp4afegvntx24a

On the expressiveness and decidability of higher-order process calculi

Ivan Lanese, Jorge A. Pérez, Davide Sangiorgi, Alan Schmitt
2011 Information and Computation  
Further, the main forms of strong bisimilarity for higher-order processes (higher-order bisimilarity, context bisimilarity, normal bisimilarity, barbed congruence) coincide.  ...  A sound and complete axiomatization of bisimilarity is given. Finally, bisimilarity is shown to become undecidable if at least four static (i.e., top-level) restrictions are added to the calculus.  ...  We are also grateful to the anonymous reviewers for their remarks and suggestions.  ... 
doi:10.1016/j.ic.2010.10.001 fatcat:m2cam7szyzac7hd7hxwbd6a6mi

On the Expressiveness and Decidability of Higher-Order Process Calculi

Ivan Lanese, Jorge A. Perez, Davide Sangiorgi, Alan Schmitt
2008 Logic in Computer Science  
Further, the main forms of strong bisimilarity for higher-order processes (higher-order bisimilarity, context bisimilarity, normal bisimilarity, barbed congruence) coincide.  ...  A sound and complete axiomatization of bisimilarity is given. Finally, bisimilarity is shown to become undecidable if at least four static (i.e., top-level) restrictions are added to the calculus.  ...  We are also grateful to the anonymous reviewers for their remarks and suggestions.  ... 
doi:10.1109/lics.2008.8 dblp:conf/lics/LanesePSS08 fatcat:c2736otrnjfixftiu2ns65q6r4

Verification of Infinite State Systems [chapter]

Ahmed Bouajjani
2003 Lecture Notes in Computer Science  
Both process algebras (or term rewriting systems) and automata (or finite control machines) are being used as specification formalisms.  ...  Verification methods can be deductive (based on the use of theorem provers), or algorithmic (based on decision or semi-decision procedures).  ...  PN FSA BPA PDA BPP multiset rewriting rewriting prefix string  ... 
doi:10.1007/978-3-540-45220-1_7 fatcat:4j5lzdbfc5hd7ptdo4tpwvmd2m

On the Complexity of Bisimulation Problems for Basic Parallel Processes [chapter]

Richard Mayr
2000 Lecture Notes in Computer Science  
Strong bisimilarity of Basic Parallel Processes (BPP) is decidable, but the best known algorithm has non-elementary complexity [7] . On the other hand, no lower bound for the problem was known.  ...  We improve this result by showing that weak bisimilarity of BPP is p 2 -hard.  ...  F for some w 2 Act . Fig. 1. A hierarchy of PRS Various subclasses of process rewrite systems can be obtained by imposing certain restrictions on the form of rules.  ... 
doi:10.1007/3-540-45022-x_29 fatcat:tnd2riqm35f4bcio42aobhayke

Highly Undecidable Questions for Process Algebras

Petr Jancar, Jirí Srba
2004 BRICS Report Series  
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).  ...  We also show Pi^1_1-hardness of weak omega-trace equivalence for the (sub)classes BPA (basic process algebra) and BPP (basic parallel processes).  ...  Such a PDA system generates a labelled transition system where Q × Γ * is the set of states 3 , Act is the set of actions, and the transition relation is defined by prefix-rewriting rules: (p a −→ qα)  ... 
doi:10.7146/brics.v11i8.21833 fatcat:etmvtxf2gzbbtbcjddqxqa27um

Note on Undecidability of Bisimilarity for Second-Order Pushdown Processes [article]

Petr Jančar, Jiří Srba
2013 arXiv   pre-print
Broadbent and Göller (FSTTCS 2012) proved the undecidability of bisimulation equivalence for processes generated by epsilon-free second-order pushdown automata.  ...  We add a few remarks concerning the used proof technique, called Defender's forcing, and the related undecidability proof for first-order pushdown automata with epsilon-transitions (Jančar and Srba, JACM  ...  (In [2] , there are used the rules q u ⊥ e −→ ε, q v ⊥ e −→ ε in the context of prefix-rewrite system definition.)  ... 
arXiv:1303.0780v1 fatcat:kxtaimjrn5bibe3ysk7gbr7gke

Recursive Ping-Pong Protocols

Hans Hüttel, Jirí Srba
2003 BRICS Report Series  
Here, our main results are that reachability and, under certain conditions, also strong bisimilarity become decidable.  ...  Our main result is that our channel-free and memory-less calculus is Turing powerful, assuming that at least three principals are involved.  ...  Bisimilarity is undecidable for ping-pong protocols of width 3 for any knowledge function which respects structural congruence and renaming of process constants.  ... 
doi:10.7146/brics.v10i47.21819 fatcat:hlcfqki34bgezhybqoz2xso5oe

Actions speak louder than words: proving bisimilarity for context-free processes

H Huttel
1998 Journal of Logic and Computation  
We also show how to obtain a sound and complete sequent-based equational theory for such processes from the tableau system and how one can extract what Caucal calls a fundamental relation from a successful  ...  Baeten, Bergstra, and Klop (and later Caucal) have proved the remarkable result that bisimulation equivalence is decidable for irredundant context-free grammars.  ...  As the strong behavioural equivalences are special cases of their weak counterparts, it is clear by the results of 17] that all weak equivalences other than bisimilarity are undecidable for normed BPA  ... 
doi:10.1093/logcom/8.4.485 fatcat:sfffqqvwdbfmjpicymyaojyms4

Refining the Process Rewrite Systems Hierarchy via Ground Tree Rewrite Systems

Stefan Göller, Anthony Widjaja Lin
2014 ACM Transactions on Computational Logic  
Among others, this connection allows us to give new insights into the decidability results for subclasses of PRS, e.g., simpler proofs of known decidability results of verifications problems on PAD.  ...  Furthermore, model checking general LTL properties is undecidable for both PA-processes and GTRS [7, 24] .  ...  Acknowledgment: We thank Taolue Chen, Matthew Hague, Jean Christoph Jung, Richard Mayr, Colin Stirling, and anonymous reviewers for their comments. Anthony W. Lin is supported by EPSRC (EP/H026878/1).  ... 
doi:10.1145/2629679 fatcat:myhh5aypjvbq3g2dy55k2onxsy

Refining the Process Rewrite Systems Hierarchy via Ground Tree Rewrite Systems [chapter]

Stefan Göller, Anthony Widjaja Lin
2011 Lecture Notes in Computer Science  
Among others, this connection allows us to give new insights into the decidability results for subclasses of PRS, e.g., simpler proofs of known decidability results of verifications problems on PAD.  ...  Furthermore, model checking general LTL properties is undecidable for both PA-processes and GTRS [7, 24] .  ...  Acknowledgment: We thank Taolue Chen, Matthew Hague, Jean Christoph Jung, Richard Mayr, Colin Stirling, and anonymous reviewers for their comments. Anthony W. Lin is supported by EPSRC (EP/H026878/1).  ... 
doi:10.1007/978-3-642-23217-6_36 fatcat:o337fmgdqfgjzaiclycp3uohnq

Completeness Results for Undecidable Bisimilarity Problems

Jiřı́ Srba
2004 Electronical Notes in Theoretical Computer Science  
The results imply Σ 1 1 -completeness of weak bisimilarity for Petri nets and give a negative answer to the open problem stated by Jančar (CAAP'95): "does the problem of weak bisimilarity for Petri nets  ...  We establish Σ 1 1 -completeness (in the analytical hierarchy) of weak bisimilarity checking for infinite-state processes generated by pushdown automata and parallel pushdown automata.  ...  Acknowledgment I would like to thank Moshe Vardi for drawing my attention to the topic, Petr Jančar for many comments and suggestions, and the anonymous referees for their remarks.  ... 
doi:10.1016/j.entcs.2003.10.003 fatcat:gpcpi7l4cvh75h6rzjoaguz2ke
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