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Equivalences of Pushdown Systems Are Hard [chapter]

Petr Jančar
2014 Lecture Notes in Computer Science  
A fundamental behavioural equivalence is bisimulation equivalence, also called bisimilarity; roughly speaking, two states of a system (or of two systems) are bisimilar if performing an action a in one  ...  We note that the known complexity lower bound for DPDA equivalence is just P-hardness (derived from P-hardness of the emptiness problem for context-free languages).  ...  The Ackermann-hardness result was achieved during my visit at LSV ENS Cachan, and I am grateful to Sylvain Schmitz and Philippe Schnoebelen for fruitful discussions.  ... 
doi:10.1007/978-3-642-54830-7_1 fatcat:ywmhwgeoqrcsjh7fpgxpvxjkl4

On the Complexity of Bisimulation Problems for Pushdown Automata [chapter]

Richard Mayr
2000 Lecture Notes in Computer Science  
All bisimulation problems for pushdown automata are at least PSPACE-hard.  ...  In particular, we show that (1) Weak bisimilarity of pushdown automata and nite automata is PSPACE-hard, even for a small xed nite automaton, (2) Strong bisimilarity of pushdown automata and nite automata  ...  The problem of bisimulation equivalence is related to the problem of language equivalence for deterministic systems, e.g., the problem of language equivalence for deterministic pushdown automata (dPDA)  ... 
doi:10.1007/3-540-44929-9_33 fatcat:zzethlkjdrchrd2deoxr5eifx4

Visibly Pushdown Automata: From Language Equivalence to Simulation and Bisimulation [chapter]

Jiří Srba
2006 Lecture Notes in Computer Science  
Our main results are that all the mentioned equivalences and preorders are EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly one-counter automata and P-complete on visibly BPA.  ...  We investigate the possibility of (bi)simulation-like preorder/equivalence checking on the class of visibly pushdown automata and its natural subclasses visibly BPA (Basic Process Algebra) and visibly  ...  My thanks go also to the referees of CSL'06 for their useful comments and for suggesting the P-hardness proof of regularity checking for vPDA and vBPA.  ... 
doi:10.1007/11874683_6 fatcat:nk77bhingvf6rmftggjjw5blkm

Beyond Language Equivalence on Visibly Pushdown Automata

Jiří Srba, Colin Stirling
2009 Logical Methods in Computer Science  
Our main results are that all the mentioned equivalences and preorders are EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly one-counter automata and P-complete on visibly BPA.  ...  We study (bi)simulation-like preorder/equivalence checking on the class of visibly pushdown automata and its natural subclasses visibly BPA (Basic Process Algebra) and visibly one-counter automata.  ...  My thanks go also to the anonymous referees of CSL'06 and LMCS for their useful comments and for suggesting the P-hardness proof of regularity checking for vBPA.  ... 
doi:10.2168/lmcs-5(1:2)2009 fatcat:6654h7yihvesfky3pzi53ae45i

Visibly Pushdown Automata: From Language Equivalence to Simulation and Bisimulation

Jirí Srba
2006 BRICS Report Series  
Our main results are that all the mentioned equivalences and preorders are EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly one-counter automata and P-complete on visibly BPA.  ...  We investigate the possibility of (bi)simulation-like preorder/equivalence checking on the class of visibly pushdown automata and its natural subclasses visibly BPA (Basic Process Algebra) and visibly  ...  My thanks go also to the referees of CSL'06 for their useful comments and for suggesting the P-hardness proof of regularity checking for vPDA and vBPA.  ... 
doi:10.7146/brics.v13i13.21918 fatcat:vaw6g2rcengijlzht26zre5v3i

An analysis of the nonemptiness problem for classes of reversal-bounded multicounter machines

Rodney R. Howell, Louis E. Rosier
1987 Journal of computer and system sciences (Print)  
This algorithm executes in time polynomial in the size of the input and the number of reversals the counters are allowed.  ...  In addition, we explore the changes in the complexity of the nonemptiness problem for these classes as different parameters are fixed or are given in either unary or binary.  ...  The equivalence problem is the problem of deciding if the languages accepted by two given machines M, and M, are equivalent.  ... 
doi:10.1016/0022-0000(87)90005-5 fatcat:sgpxwc4ypfg5ngpcsxpcldo5be

Visibly linear dynamic logic

Alexander Weinert, Martin Zimmermann
2018 Theoretical Computer Science  
The main technical contribution of this work is a translation of VLDL into ω-visibly pushdown automata of exponential size via one-way alternating jumping automata.  ...  We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words.  ...  The authors would like to thank Laura Bozzelli for providing the full version of [4] and Christof Löding for pointing out the 3ExpTime-hardness of solving infinite games for visibly pushdown games against  ... 
doi:10.1016/j.tcs.2018.06.030 fatcat:ua2ubox6irajvazrmvfueztzta

On the Power of Labels in Transition Systems [chapter]

Jiří Srba
2001 Lecture Notes in Computer Science  
We apply the reduction to the class of transition systems generated by Petri nets and pushdown automata, and obtain several decidability/complexity corollaries for unlabelled systems.  ...  Bisimilarity checking problem between an unlabelled and normed Petri net and a finite-state system is EXPSPACE-hard.  ...  There are two central questions about decidability (complexity) of equivalence and model checking problems: -Equivalence checking (see [Mol96] ): Given two (infinite-state) systems, are they equal with  ... 
doi:10.1007/3-540-44685-0_19 fatcat:vz2pettxn5huvn65e7fm3kjpfe

On the complexity of checking semantic equivalences between pushdown processes and finite-state processes

Antonín Kučera, Richard Mayr
2010 Information and Computation  
Crown In this paper we consider pushdown processes, the class of processes whose behavior is definable by pushdown automata (PDA), as well as finite-state systems, the class of processes which are definable  ...  Thus, most equivalence checking problems between PDA and finite-state systems are fixed-parameter tractable.  ...  Checking weak bisimilarity of pushdown processes and finite-state systems is PSPACE-hard, even for the fixed finite-state system F of Fig. 4 . Proof.  ... 
doi:10.1016/j.ic.2010.01.003 fatcat:6j63efjbnbh4ngrksqyzcecmnu

Complexity results for prefix grammars

Markus Lohrey, Holger Petersen
2005 RAIRO - Theoretical Informatics and Applications  
Resolving an open problem of Ravikumar and Quan, we show that equivalence of prefix grammars is complete in PSPACE.  ...  We also show that membership for these grammars is complete in P (it was known that this problem is in P) and characterize the complexity of equivalence and inclusion for monotonic grammars.  ...  There is a well-known correspondence between prefix grammars and pushdown systems, see [4, 9] .  ... 
doi:10.1051/ita:2005024 fatcat:woakj5qpdbb7pobrf6drgwypdu

ROADMAP OF INFINITE RESULTS [chapter]

JIŘÍ SRBA
2004 Current Trends in Theoretical Computer Science  
This paper provides a comprehensive summary of equivalence checking results for infinite-state systems.  ...  The most recent version of this document is available from the web-page  ...  I would like to thank IvanaČerná, Petr Jančar, Antonín Kučera, Mogens Nielsen and Paulo Borges Oliva for reading a draft of this paper.  ... 
doi:10.1142/9789812562494_0054 fatcat:n7gd7hufhjhgvjrszmclz7vedy

On the Complexity of Semantic Equivalences for Pushdown Automata and BPA [chapter]

Antonín Kučera, Richard Mayr
2002 Lecture Notes in Computer Science  
We study the complexity of comparing pushdown automata (PDA) and context-free processes (BPA) to finite-state systems, w.r.t. strong and weak simulation preorder/equivalence and strong and weak bisimulation  ...  The problems PDA ⊑ FS, FS ⊑ PDA, PDA ≃ FS are EXPTIME -hard even for a fixed finite-state system. Moreover, we show EXPTIMEhardness of the PDA ∼ PDA problem.  ...  checking bisimilarity of two pushdown systems is EXPTIME -hard.  ... 
doi:10.1007/3-540-45687-2_36 fatcat:yfz36qr2wvhmvmf7gw4m5w42xq

Visibly Linear Dynamic Logic [article]

Alexander Weinert, Martin Zimmermann
2017 arXiv   pre-print
The main technical contribution of this work is a translation of VLDL into ω-visibly pushdown automata of exponential size via one-way alternating jumping automata.  ...  We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words.  ...  Acknowledgements The authors would like to thank Laura Bozzelli for providing the full version of [4] and Christof Löding for pointing out the 3Ex-pTime-hardness of solving infinite games for visibly  ... 
arXiv:1512.05177v2 fatcat:f6uldf5zcvcc5craj7nos4s4pm

Bisimulation Equivalence of First-Order Grammars is ACKERMANN-Complete [article]

Petr Jančar, Sylvain Schmitz
2019 arXiv   pre-print
Checking whether two pushdown automata with restricted silent actions are weakly bisimilar was shown decidable by S\'enizergues (1998, 2005).  ...  We provide the first known complexity upper bound for this famous problem, in the equivalent setting of first-order grammars.  ...  Jančar acknowledges the support of the Grant Agency of Czech Rep., GAČR 18-11193S; part of this research was conducted while he held an invited professorship at ENS Paris-Saclay. S.  ... 
arXiv:1901.07170v1 fatcat:nkfrem6yave6dmom27zakbatlm

Extended Computation Tree Logic [chapter]

Roland Axelsson, Matthew Hague, Stephan Kreutzer, Martin Lange, Markus Latte
2010 Lecture Notes in Computer Science  
In addition, we analyse the complexity of satisfiability and compare the expressive power of these logics to CTL* and extensions of PDL.  ...  We introduce a generic extension of the popular branching-time logic CTL which refines the temporal until and release operators with formal languages.  ...  Model checking visibly pushdown systems against CTL[DFA] is hard for EXPTIME, EG[NFA] is hard for 2EXPTIME, and EF[DPDA] and EG[DPDA] are undecidable. Theorem 6.5.  ... 
doi:10.1007/978-3-642-16242-8_6 fatcat:4pvdbae6fbdkpmtiha4mnlrzyy
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