Simulation Problems Over One-Counter Nets

Hofman, Piotr; Lasota, Sławomir; Mayr, Richard; Totzke, Patrick

doi:10.2168/lmcs-12(1:6)2016

Cited by 7 publications

(16 citation statements)

References 13 publications

(23 reference statements)

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“…The basic versions are unary, where the counter can be incremented and decremented by one in one step, while in the succinct versions the possible changes can be arbitrary integers Our contribution. In this paper we close a complexity gap for the simulation problem on succinct OCN that was mentioned in [13], noting that there was a PSPACE lower bound and an EXPSPACE upper bound for the problem. We show EXPSPACE-hardness (and thus EXPSPACE-completeness) of the problem, using a defender-choice technique (cf., e.g., [19]) to reduce reachability games to any relation between simulation preorder and bisimulation equivalence.…”

Section: Introductionmentioning

confidence: 61%

“…We simplify the proof of the theorem from [17] substantially, while also highlighting a new useful observation, called the black-white vector travel. In Subsection 5.2 we prove the detailed belt theorem that presents the slopes and the widths of belts by small integers and is in principle equivalent to the respective theorem proved in [13]. Our proof is conceptually different than the proof in [13], due to another use of the black-white vector travel.…”

Section: Structure Of Simulation Preorder On One-counter Netsmentioning

confidence: 84%

“…Recalling the EXPSPACE-hardness of Socn-Rg (from [14], or from the stronger statement of Theorem 1), the respective lemmas (Lemma 6 and 7) will yield the following theorem (which also answers the respective open question from [13]):…”

Section: Reachability Game Reduces To (Bi)simulation Gamementioning

confidence: 96%

“…Based on the basic belt theorem, a straightforward algorithm that decides whether p(m) q(n) for a given OCN N , or more generally constructs a description of on the LTS L N , was given in [17,15]; taking the "polynomial" slopes and widths of belts into ac-count, we get polynomial-space algorithms [13]. In principle, we can use "brute force" and simply construct an initial rectangle of the planes N × N, first assuming that all points are black and stepwise recolouring to white when finding points with ranks 1, 2, .…”

Section: Polynomial-space Algorithmmentioning

confidence: 99%

“…count, we get polynomial-space algorithms [13]. In principle, we can use "brute force" and simply construct an initial rectangle of the planes N × N, first assuming that all points are black and stepwise recolouring to white when finding points with ranks 1, 2, .…”

Section: Remark On Double-exponential Periodsmentioning

confidence: 99%

See 4 more Smart Citations

EXPSPACE-Complete Variant of Countdown Games, and Simulation on Succinct One-Counter Nets

Jancar

Osicka

Sawa

2018

Lecture Notes in Computer Science

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We answer an open complexity question by Hofman, Lasota, Mayr, Totzke (LMCS 2016) [HLMT16] for simulation preorder of succinct one-counter nets (i.e., one-counter automata with no zero tests where counter increments and decrements are integers written in binary), by showing that all relations between bisimulation equivalence and simulation preorder are EXPSPACE-hard for these nets. We describe a reduction from reachability games whose EXPSPACE-completeness in the case of succinct one-counter nets was shown by Hunter [RP 2015], by using other results. We also provide a direct self-contained EXPSPACE-completeness proof for a special case of such reachability games, namely for a modification of countdown games that were shown EXPTIME-complete by Jurdzinski, Sproston, Laroussinie [LMCS 2008]; in our modification the initial counter value is not given but is freely chosen by the first player. We also present a new simplified proof of the belt theorem that gives a simple graphic presentation of simulation preorder on one-counter nets and leads to a polynomial-space algorithm; it is an alternative to the proof from [HLMT16].

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Section: Introductionmentioning

confidence: 61%

Section: Structure Of Simulation Preorder On One-counter Netsmentioning

confidence: 84%

Section: Reachability Game Reduces To (Bi)simulation Gamementioning

confidence: 96%

Section: Polynomial-space Algorithmmentioning

confidence: 99%

Section: Remark On Double-exponential Periodsmentioning

confidence: 99%

See 3 more Smart Citations

EXPSPACE-Complete Variant of Countdown Games, and Simulation on Succinct One-Counter Nets

Jancar

Osicka

Sawa

2018

Lecture Notes in Computer Science

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On History-Deterministic One-Counter Nets

Prakash

Thejaswini

2023

Lecture Notes in Computer Science

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We consider the model of history-deterministic one-counter nets (OCNs). History-determinism is a property of transition systems that allows for a limited kind of non-determinism which can be resolved ‘on-the-fly’. Token games, which have been used to characterise history-determinism over various models, also characterise history-determinism over OCNs. By reducing 1-token games to simulation games, we are able to show that checking for history-determinism of OCNs is decidable. Moreover, we prove that this problem is $$\textbf{PSPACE}$$ PSPACE -complete for a unary encoding of transitions, and $$\textbf{EXPSPACE}$$ EXPSPACE -complete for a binary encoding and undecidable for one-counter automata (OCA), which are OCNs that can test for zeroes.We then study the language properties of history-deterministic OCNs. We show that the resolvers of non-determinism for history-deterministic OCNs are eventually periodic. As a consequence, for a given history-deterministic OCN, we construct a language equivalent deterministic OCA. We also show the decidability of comparing languages of history-deterministic OCNs, such as language inclusion and language universality.

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MTL and TPTL for One-Counter Machines

Feng

Carapelle

Gil

et al. 2019

ACM Trans. Comput. Logic

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Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) are quantitative extensions of Linear Temporal Logic (LTL) that are prominent and widely used in the verification of real-timed systems. We study MTL and TPTL as specification languages for one-counter machines. It is known that model checking one-counter machines against formulas of Freeze LTL (FLTL), a strict fragment of TPTL, is undecidable. We prove that in our setting, MTL is strictly less expressive than TPTL, and incomparable in expressiveness to FLTL, so undecidability for MTL is not implied by the result for FLTL. We show, however, that the model-checking problem for MTL is undecidable. We further prove that the satisfiability problem for the unary fragments of TPTL and MTL are undecidable; for TPTL, this even holds for the fragment in which only one register and the finally modality is used. This is opposed to a known decidability result for the satisfiability problem for the same fragment of FLTL.

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Simulation Problems Over One-Counter Nets

Cited by 7 publications

References 13 publications

EXPSPACE-Complete Variant of Countdown Games, and Simulation on Succinct One-Counter Nets

EXPSPACE-Complete Variant of Countdown Games, and Simulation on Succinct One-Counter Nets

On History-Deterministic One-Counter Nets

MTL and TPTL for One-Counter Machines

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