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## A Polynomial Time Algorithm for Deciding Branching Bisimilarity on Totally Normed BPA (2014)

### Citations

4808 |
Introduction to Automata Theory, Languages, and Computation
- Hopcroft, Ullman
- 1979
(Show Context)
Citation Context ...roved a surprising result that strong bisimilarity on normed BPA is decidable. This result is in sharp contrast to the classical fact that language equivalence is undecidable for context free grammar =-=[15]-=-. After this remarkable discovery, decidability and complexity issues of bisimilarity checking on infinite state systems have been intensively investigated. See [19,6,28,29,20] for a number of surveys... |

3935 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ... BPA is exactly realtime normed BPA. Bisimulations and Bisimilarities In the presence of silent actions two well known process equalities are the branching bisimilarity [31] and the weak bisimilarity =-=[26]-=-. Definition 1. Let R be a relation on processes. R is a branching bisimulation, if the following hold whenever αRβ: 1. If α ℓ −→ α′, then either (a) ℓ = τ and α′Rβ; or (b) β =⇒ β′′ ℓ −→ β′ and α′Rβ′ ... |

329 | Branching Time and Abstraction in Bisimulation Semantics
- Glabbeek, Weijland
- 1996
(Show Context)
Citation Context ... In the presence of silent actions the picture is less clear. Even the decidability for weak bisimilarity is still open. A remarkable discovery is made by Fu [11] recently that branching bisimilarity =-=[31]-=-, a standard refined alternative of weak bisimilarity, is decidable on normed BPA. Very recently, Czerwiński and Jančar confirm this problem to be in NEXPTIME [9]. The current best lowerbound for we... |

253 | Process Algebra
- Baeten, Weijland
- 1990
(Show Context)
Citation Context ...y defined refinement operation fitted for our algorithm and the proposal of elaborately developed techniques, which are quite different from previous works. 1 Introduction Basic process algebra (BPA) =-=[2]-=- is a fundamental model of infinite state systems, with its famous counterpart in the theory of formal languages: context free grammars in Greibach normal forms, which generate the entire context free... |

104 |
Decidability of bisimulation equivalence for processes generating context-free languages,”
- Baeten, Bergstra, et al.
- 1993
(Show Context)
Citation Context ...ms, with its famous counterpart in the theory of formal languages: context free grammars in Greibach normal forms, which generate the entire context free languages. In 1987, Baeten, Bergstra and Klop =-=[3,4]-=- proved a surprising result that strong bisimilarity on normed BPA is decidable. This result is in sharp contrast to the classical fact that language equivalence is undecidable for context free gramma... |

89 | Verification of infinite structures
- Burkart, Caucal, et al.
- 2001
(Show Context)
Citation Context ...decidable for context free grammar [15]. After this remarkable discovery, decidability and complexity issues of bisimilarity checking on infinite state systems have been intensively investigated. See =-=[19,6,28,29,20]-=- for a number of surveys. As regards to the strong bisimilarity checking on normed BPA, Hüttel and Stirling [17] improved the result of Baeten, Bergstra and Klop using a more simplified proof by rela... |

58 | A polynomial algorithm for deciding bisimilarity of normed context-free processes.
- Hirshfeld, Jerrum, et al.
- 1996
(Show Context)
Citation Context ...ystem. Later, Huynh and Tian [18] showed that the problem is in ΣP2 , the second level of the polynomial hierarchy. Before long, another significant discovery was made by Hirshfeld, Jerrum and Moller =-=[13]-=- who showed that the problem can even be decided in polynomial time, with the complexity O(N13). The running time was later improved [21,10]. All these algorithms take the approach of partition refine... |

47 | Actions speak louder than words: Proving bisimilarity for context-free processes
- Hüttel, Stirling
- 1991
(Show Context)
Citation Context ... checking on infinite state systems have been intensively investigated. See [19,6,28,29,20] for a number of surveys. As regards to the strong bisimilarity checking on normed BPA, Hüttel and Stirling =-=[17]-=- improved the result of Baeten, Bergstra and Klop using a more simplified proof by relating the strong bisimilarity of two normed BPA processes to the existence of a successful tableau system. Later, ... |

41 | Branching bisimilarity is an equivalence indeed
- Basten
- 1996
(Show Context)
Citation Context ...congruence relations for (t)nBPA. We remark that transitivity of≃ is not straightforward according to Definition 1, because the branching bisimulation R defined in Definition 1 need not be transitive =-=[5]-=-. To solve this problem, van Glabbeek and Weijland [31] introduce a slightly different notion called semi-branching bisimulation. Definition 3. Let R be a relation on processes. R is a semi-branching ... |

35 | An improved pattern matching algorithm for strings in terms of straight-line programs
- Miyazaki, Shinohara, et al.
- 1997
(Show Context)
Citation Context ...rely on an efficient implementation of equality checking on SLP-compressed strings, which is typically implemented (as a special case) by an efficient algorithm of compressed pattern matching such as =-=[27,22]-=-. Lohrey [23] gives a nice survey on algorithms on SLP-compressed strings. One deficiency of the above scheme is that the procedure for string equality checking is called every time two strings need t... |

19 | Maintaining dynamic sequences under equality tests in polylogarithmic time.
- Mehlhorn, Sundar, et al.
- 1997
(Show Context)
Citation Context ...d strings. One deficiency of the above scheme is that the procedure for string equality checking is called every time two strings need to compare, and previous computations are completely ignored. In =-=[25]-=- and its improved version [1], a data structure for finite set of strings is maintained, which supports concatenation, splitting, and equality checking operations. Czerwiński [7] uses this technique ... |

18 |
Bisimulation trees and the decidability of weak bisimulations
- Hirshfeld
- 1996
(Show Context)
Citation Context ... construction developed in [17] for branching bisimilarity on totally normed BPA. Although Hüttel’s construction is not sound for weak bisimilarity, the relevant decidability can also be established =-=[12]-=-. For the lower bound, NP-hardness is established by Stř́ıbrná [30] for weak bisimilarity via a reduction from the knapsack problem. By inspecting Stř́ıbrná’s proof, we are aware that the NP-hardn... |

15 | Equivalence-checking on infinite-state systems: Techniques and results.
- Kucera, Jancar
- 2006
(Show Context)
Citation Context ...decidable for context free grammar [15]. After this remarkable discovery, decidability and complexity issues of bisimilarity checking on infinite state systems have been intensively investigated. See =-=[19,6,28,29,20]-=- for a number of surveys. As regards to the strong bisimilarity checking on normed BPA, Hüttel and Stirling [17] improved the result of Baeten, Bergstra and Klop using a more simplified proof by rela... |

14 | A polynomial-time algorithm for deciding bisimulation equivalence of normed basic parallel processes.
- Hirshfeld, Jerrum, et al.
- 1996
(Show Context)
Citation Context ...te a different refinement scheme. This refinement scheme was previously used in developing an polynomial-time algorithm of checking strong bisimilarity on normed basic parallel processes (normed BPP) =-=[14]-=-. In this way Czerwiński and Lasota improve the running time to O(N5). Hitherto, the best algorithm was reported in [7], whose running time is O(N4polylog(N)). In the presence of silent actions the p... |

11 |
Deciding bisimilarity of normed context-free pro- cesses is
- Huynh, Tian
- 1994
(Show Context)
Citation Context ...esult of Baeten, Bergstra and Klop using a more simplified proof by relating the strong bisimilarity of two normed BPA processes to the existence of a successful tableau system. Later, Huynh and Tian =-=[18]-=- showed that the problem is in ΣP2 , the second level of the polynomial hierarchy. Before long, another significant discovery was made by Hirshfeld, Jerrum and Moller [13] who showed that the problem ... |

10 | Algorithmics on SLP-compressed strings: a survey,
- Lohrey
- 2012
(Show Context)
Citation Context ...ient implementation of equality checking on SLP-compressed strings, which is typically implemented (as a special case) by an efficient algorithm of compressed pattern matching such as [27,22]. Lohrey =-=[23]-=- gives a nice survey on algorithms on SLP-compressed strings. One deficiency of the above scheme is that the procedure for string equality checking is called every time two strings need to compare, an... |

9 | Faster algorithm for bisimulation equivalence of normed context-free processes
- Lasota, Rytter
(Show Context)
Citation Context ...significant discovery was made by Hirshfeld, Jerrum and Moller [13] who showed that the problem can even be decided in polynomial time, with the complexity O(N13). The running time was later improved =-=[21,10]-=-. All these algorithms take the approach of partition refinement, relying on the unique decomposition property and some efficient way of equality checking on compressed long strings. It deserves speci... |

7 | Fast equivalence-checking for normed context-free processes,” in
- Czerwinski, Lasota
- 2010
(Show Context)
Citation Context ...which is not known before. The algorithm takes the partition refinement approach and the final implementation can be thought of as a generalization of the previous algorithm of Czerwiński and Lasota =-=[10,7]-=-. However, unexpectedly, the correctness of the algorithm cannot be directly generalized from previous works, and the correctness proof turns out to be subtle. The proof depends on the existence of a ... |

7 | Techniques for decidability and undecidability of bisimilarity
- Jančar, Moller
- 1999
(Show Context)
Citation Context ...decidable for context free grammar [15]. After this remarkable discovery, decidability and complexity issues of bisimilarity checking on infinite state systems have been intensively investigated. See =-=[19,6,28,29,20]-=- for a number of surveys. As regards to the strong bisimilarity checking on normed BPA, Hüttel and Stirling [17] improved the result of Baeten, Bergstra and Klop using a more simplified proof by rela... |

6 | Silence is golden: Branching bisimilarity is decidable for context-free processes
- Huttel
- 1991
(Show Context)
Citation Context ...PA, called totally normed BPA, in which unique decomposition property still holds for branching bisimilarity. The bisimilarity checking on totally normed BPA also has a long history. In 1991, Hüttel =-=[16]-=- repeated the tableau construction developed in [17] for branching bisimilarity on totally normed BPA. Although Hüttel’s construction is not sound for weak bisimilarity, the relevant decidability can... |

6 | Solving classical string problems an compressed texts
- Lifshits
(Show Context)
Citation Context ...rely on an efficient implementation of equality checking on SLP-compressed strings, which is typically implemented (as a special case) by an efficient algorithm of compressed pattern matching such as =-=[27,22]-=-. Lohrey [23] gives a nice survey on algorithms on SLP-compressed strings. One deficiency of the above scheme is that the procedure for string equality checking is called every time two strings need t... |

6 |
Roadmap of infinite results. In: Current Trends In
- Srba
- 2004
(Show Context)
Citation Context |

6 |
Hardness results for weak bisimilarity of simple process algebras
- Stribrna
- 1998
(Show Context)
Citation Context ... normed BPA. Although Hüttel’s construction is not sound for weak bisimilarity, the relevant decidability can also be established [12]. For the lower bound, NP-hardness is established by Stř́ıbrná =-=[30]-=- for weak bisimilarity via a reduction from the knapsack problem. By inspecting Stř́ıbrná’s proof, we are aware that the NP-hardness still holds for any other bisimilarity, such as delay bisimilarit... |

5 |
Weak bisimilarity and regularity of context-free processes is exptime-hard
- Mayr
- 2005
(Show Context)
Citation Context ...cidable on normed BPA. Very recently, Czerwiński and Jančar confirm this problem to be in NEXPTIME [9]. The current best lowerbound for weak bisimilarity is the EXPTIME-hardness established by Mayr =-=[24]-=-, whose proof can be slightly modified to show the EXPTIME-hardness for branching bisimilarity as well. In retrospect one cannot help thinking that more attention should have been paid to the branchin... |

4 | S.: Decidability of branching bisimulation on normed commutative context-free processes. Theory Comput
- Czerwinski, Hofman, et al.
- 2014
(Show Context)
Citation Context ...esults for weak bisimilarity still hold for branching bisimilarity. 30 There are two remarkable exceptions. The decidability of branching bisimilarity is established by Czerwiński, Hofman and Lasota =-=[8]-=- on normed BPP, and by Fu [11] on normed BPA. In these two cases, decidability of weak bisimilarity is unknown. Recently, we have proven that branching (and weak) bisimilarity is undecidable on every ... |

4 |
On the computational complexity of bisimulation, redux
- Moller, Smolka, et al.
(Show Context)
Citation Context |

3 |
Stølting Brodal, and Theis Rauhe. Pattern matching in dynamic texts
- Alstrup, Gerth
- 2000
(Show Context)
Citation Context ...he above scheme is that the procedure for string equality checking is called every time two strings need to compare, and previous computations are completely ignored. In [25] and its improved version =-=[1]-=-, a data structure for finite set of strings is maintained, which supports concatenation, splitting, and equality checking operations. Czerwiński [7] uses this technique to improve his previous algor... |

3 |
Checking equality and regularity for normed BPA with silent moves
- Fu
(Show Context)
Citation Context ...still hold for branching bisimilarity. 30 There are two remarkable exceptions. The decidability of branching bisimilarity is established by Czerwiński, Hofman and Lasota [8] on normed BPP, and by Fu =-=[11]-=- on normed BPA. In these two cases, decidability of weak bisimilarity is unknown. Recently, we have proven that branching (and weak) bisimilarity is undecidable on every model above BPA and BPP in the... |

2 |
Partially-commutative context-free graphs
- Czerwiński
- 2013
(Show Context)
Citation Context ...which is not known before. The algorithm takes the partition refinement approach and the final implementation can be thought of as a generalization of the previous algorithm of Czerwiński and Lasota =-=[10,7]-=-. However, unexpectedly, the correctness of the algorithm cannot be directly generalized from previous works, and the correctness proof turns out to be subtle. The proof depends on the existence of a ... |

1 |
Branching bisimilarity of normed BPA processes is
- Czerwinski, Jancar
- 2014
(Show Context)
Citation Context ...cently that branching bisimilarity [31], a standard refined alternative of weak bisimilarity, is decidable on normed BPA. Very recently, Czerwiński and Jančar confirm this problem to be in NEXPTIME =-=[9]-=-. The current best lowerbound for weak bisimilarity is the EXPTIME-hardness established by Mayr [24], whose proof can be slightly modified to show the EXPTIME-hardness for branching bisimilarity as we... |

1 |
Yuxi Fu, Chaodong He, Mingzhang Huang, and Xiuting Tao. Branching bisimilarity checking for prs
- Yin
- 2014
(Show Context)
Citation Context ...idability of weak bisimilarity is unknown. Recently, we have proven that branching (and weak) bisimilarity is undecidable on every model above BPA and BPP in the PRS hierarchy even in the normed case =-=[32]-=-. It is believed that branching bisimilarity is easier to decide than weak bisimilarity. Currently, there is no real instance to support this belief. This paper provides an interesting instance. We ex... |