Decidability of Weak Simulation on One-Counter Nets

One-counter nets (OCN) are Petri nets with exactly one unbounded place. They are equivalent to a subclass of one-counter automata with only a weak test for zero. We show that weak simulation preorder is decidable for OCN and that weak simulation approximants do not converge at level ω, but only at ω2. In contrast, other semantic relations like weak bisimulation are undecidable for OCN [1], and so are weak (and strong) trace inclusion (Sec. VII).

[1]  Anthony Widjaja Lin,et al.  On the Computational Complexity of Verifying One-Counter Processes , 2009, 2009 24th Annual IEEE Symposium on Logic In Computer Science.

[2]  Albert R. Meyer,et al.  The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space , 1972, SWAT.

[3]  R. V. Glabbeek.  The Linear Time-Branching Time Spectrum I The Semantics of Concrete , Sequential ProcessesR , 2007 .

[4]  Géraud Sénizergues,et al.  Decidability of bisimulation equivalence for equational graphs of finite out-degree , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[5]  Olivier Serre,et al.  Parity Games Played on Transition Graphs of One-Counter Processes , 2006, FoSSaCS.

[6]  Antonín Kucera,et al.  Why Is Simulation Harder than Bisimulation? , 2002, CONCUR.

[7]  Parosh Aziz Abdulla,et al.  Simulation Is Decidable for One-Counter Nets (Extended Abstract) , 1998, CONCUR.

[8]  Faron Moller,et al.  Simulation Problems for One-Counter Machines , 1999, SOFSEM.

[9]  Faron Moller,et al.  Simulation and Bisimulation over One-Counter Processes , 2000, STACS.

[10]  Petr Jancar.  Undecidability of Bisimilarity for Petri Nets and Some Related Problems , 1995, Theor. Comput. Sci..

[11]  P. Abdulla,et al.  Simulation Is Decidable for One-Counter Nets , 2022 .

[12]  Petr Jancar,et al.  P-Hardness of Equivalence Testing on Finite-State Processes , 2001, SOFSEM.

[13]  Antonín Kucera,et al.  On Simulation-Checking with Sequential Systems , 2000, ASIAN.

[14]  Faron Moller,et al.  Petri Nets and Regular Processes , 1999, J. Comput. Syst. Sci..

[15]  Stanislav Böhm,et al.  Bisimilarity of One-Counter Processes Is PSPACE-Complete , 2010, CONCUR.

[16]  Jirí Srba.  Beyond Language Equivalence on Visibly Pushdown Automata , 2009, Log. Methods Comput. Sci..

[17]  Faron Moller,et al.  Simulation of One-Counter Nets via Colouring , 1999 .

[18]  Orna Kupferman,et al.  What's Decidable about Weighted Automata? , 2011, ATVA.

[19]  Richard Mayr.  Undecidability of Weak Bisimulation Equivalence for 1-Counter Processes , 2003, ICALP.

[20]  Leslie G. Valiant,et al.  Decision procedures for families of deterministic pushdown automata , 1973 .

[21]  Antonín Kucera,et al.  Efficient Verification Algorithms for One-Counter Processes , 2000, ICALP.

[22]  Hans Hüttel,et al.  Undecidable equivalences for basic parallel processes , 1994, Inf. Comput..

[23]  Kousha Etessami,et al.  Quasi-Birth-Death Processes, Tree-Like QBDs, Probabilistic 1-Counter Automata, and Pushdown Systems , 2008, 2008 Fifth International Conference on Quantitative Evaluation of Systems.

[24]  Mogens Nielsen,et al.  Decidability Issues for Petri Nets - a survey , 1994, Bull. EATCS.