Decidability of Weak Simulation on One-Counter Nets
Piotr Hofman,Richard Mayr,Patrick Totzke +2 more
- pp 203-212
TLDR
In this paper, it was shown that weak simulation preorder is decidable for one-counter automata and weak simulation approximants do not converge at level ω, but only at ω2.Abstract:
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).read more
Citations
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Book ChapterDOI
Trace Inclusion for One-Counter Nets Revisited
Piotr Hofman,Patrick Totzke +1 more
TL;DR: One-counter nets (OCN) consist of a non-deterministic finite control and a single integer counter that cannot be fully tested for zero as mentioned in this paper. But the trace inclusion problem is undecidable for OCN.
Journal ArticleDOI
Simulation Problems Over One-Counter Nets
TL;DR: One-counter nets (OCN) are automata equipped with a counter that can store non-negative integer values, and that cannot be tested for zero as discussed by the authors, and are PSPACE-complete.
Journal ArticleDOI
Simulation Problems Over One-Counter Nets
TL;DR: This work shows that both strong and weak simulation preorder on OCN are PSPACE-complete, which means these are exactly 1-dimensional vector addition systems with states.
Proceedings ArticleDOI
Simulation Over One-counter Nets is PSPACE-Complete
TL;DR: It is shown that both strong and weak simulation preorder on OCN are Pspace-complete.
Journal Article
Shortest paths in one-counter systems
TL;DR: It is shown that any one-counter automaton with n states, if its language is non-empty, accepts some word of length at most \(O(n^2)", which proves a tight upper bound on the length of shortest paths between arbitrary configurations in one- counter transition systems.
References
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Proceedings ArticleDOI
The equivalence problem for regular expressions with squaring requires exponential space
Book ChapterDOI
CHAPTER 1 – The Linear Time - Branching Time Spectrum I.* The Semantics of Concrete, Sequential Processes
TL;DR: Various semantics in the linear time - branching time spectrum are presented in a uniform, model-independent way, and for each of them a complete axiomatization is provided.
Journal ArticleDOI
Undecidability of bisimilarity for Petri nets and some related problems
TL;DR: The main result shows the undecidability of (strong) bisimilarity for labelled (place/transition) Petri nets for Semilinear bisimulations.
Dissertation
Decision Procedures for Families of Deterministic Pushdown Automata
TL;DR: It is shown that such questions as whether a deterministic context-free language can be recognised by a machine in any one of the above named classes, must be, if decidable at all, at least as difficult to decide as whether such a language is regular.