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Model Checking Freeze LTL over One-Counter Automata [chapter]

Stéphane Demri, Ranko Lazić, Arnaud Sangnier
<i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lliksjpywfcx3dtw7aj2vkybvi" style="color: black;">Foundations of Software Science and Computational Structures</a> </i> &nbsp;
We study complexity issues related to the model-checking problem for LTL with registers (a.k.a. freeze LTL) over one-counter automata.  ...  By constrast, we prove that model checking LTL with registers over nondeterministic one-counter automata is Σ 1 1 -complete [resp.  ...  -Model checking LTL with registers over deterministic one-counter automata is PSPACE-complete (see Sect. 3.2).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-78499-9_34">doi:10.1007/978-3-540-78499-9_34</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/fossacs/DemriLS08.html">dblp:conf/fossacs/DemriLS08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7mmtnnmyzbcfppd2vidp6fxqb4">fatcat:7mmtnnmyzbcfppd2vidp6fxqb4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190503023620/https://link.springer.com/content/pdf/10.1007%2F978-3-540-78499-9_34.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/18/c7/18c7d2100b243de97489f34d3026e351fbfaaf67.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-78499-9_34"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

The Complexity of Flat Freeze LTL [article]

Benedikt Bollig, Karin Quaas, Arnaud Sangnier
<span title="2019-09-27">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We consider the model-checking problem for freeze LTL on one-counter automata (OCA).  ...  In a previous work, Lechner et al. showed that model checking for flat freeze LTL on OCA with binary encoding of counter updates is decidable and in 2NEXPTIME.  ...  Introduction One-counter automata (OCA) are a simple yet fundamental computational model operating on a single counter that ranges over the non-negative integers.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1609.06124v7">arXiv:1609.06124v7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zoc35zwzzng2fb5jsngx2mihly">fatcat:zoc35zwzzng2fb5jsngx2mihly</a> </span>
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Model Checking Metric Temporal Logic over Automata with One Counter [chapter]

Karin Quaas
<span title="">2013</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Question: State of the Art: • Freeze LTL-Model Checking of deterministic 1-CM is PSpace-complete.  ...  (Demri et al. 2008) State of the Art: • Freeze LTL-Model Checking of deterministic 1-CM is Todo.  ...  Proof We define an equivalence relation ≡ over the set of configurations of M . • form the equivalence classes induced by ≡, • the index of ≡ is finite, • each equivalence class can be symbolically represented  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-37064-9_41">doi:10.1007/978-3-642-37064-9_41</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a4m6idsjxnhuja2dzhaucyiqae">fatcat:a4m6idsjxnhuja2dzhaucyiqae</a> </span>
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Model Checking Flat Freeze LTL on One-Counter Automata [article]

Antonia Lechner, Richard Mayr, Joël Ouaknine, Amaury Pouly, James Worrell
<span title="2018-10-18">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Freeze LTL is a temporal logic with registers that is suitable for specifying properties of data words. In this paper we study the model checking problem for Freeze LTL on one-counter automata.  ...  Freeze LTL on one-counter automata as an open problem.  ...  Model Checking Freeze LTL on One-Counter Automata. Freeze LTL [5] is an extension of Linear Temporal Logic that can be used to specify properties of data words.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1606.02643v4">arXiv:1606.02643v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/udpylelqircbnlceaxitbt2bfi">fatcat:udpylelqircbnlceaxitbt2bfi</a> </span>
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Safely Freezing LTL [chapter]

Ranko Lazić
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We show that, for one register, satisfiability, refinement and model checking problems are decidable. The main result in the paper is that satisfiability is ExpSpace-complete.  ...  We also show that refinement and model checking are not primitive recursive, and that dropping the safety restriction, adding past-time temporal operators, or adding one more register, each cause undecidability  ...  Register automata We shall define (one-way) alternating register automata over infinite data words, and nondeterministic register automata as a subclass.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11944836_35">doi:10.1007/11944836_35</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g4gaal5mwnea7g3zy5hmnptema">fatcat:g4gaal5mwnea7g3zy5hmnptema</a> </span>
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Model checking memoryful linear-time logics over one-counter automata

Stéphane Demri, Ranko Lazić, Arnaud Sangnier
<span title="">2010</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
We study complexity of the model-checking problems for LTL with registers (also known as freeze LTL and written LTL ↓ ) and for first-order logic with data equality tests (written FO(∼, <, +1)) over one-counter  ...  We show that model checking LTL ↓ and FO(∼, <, +1) over deterministic one-counter automata is PSpace-complete with infinite and finite accepting runs.  ...  The finitary [resp. infinitary] (existential) model-checking problem over one-counter automata for LTL with registers, denoted as MC(LTL) * [resp.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2010.02.021">doi:10.1016/j.tcs.2010.02.021</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gkuqbnuxujdfngzkflnhfo3q4e">fatcat:gkuqbnuxujdfngzkflnhfo3q4e</a> </span>
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Model checking memoryful linear-time logics over one-counter automata [article]

Stephane Demri, Ranko Lazic, Arnaud Sangnier
<span title="2010-01-18">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study complexity of the model-checking problems for LTL with registers (also known as freeze LTL) and for first-order logic with data equality tests over one-counter automata.  ...  By constrast, we prove that model checking freeze LTL in which the until operator is restricted to the eventually operator over nondeterministic one-counter automata is undecidable even if only one register  ...  The finitary [resp. infinitary] (existential) model-checking problem over one-counter automata for LTL with registers, noted MC(LTL) * [resp.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0810.5517v2">arXiv:0810.5517v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jzific7vdnhc3ggd65fald62fa">fatcat:jzific7vdnhc3ggd65fald62fa</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-0810.5517/0810.5517.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1e/7b/1e7bf2ecc7224474f06d7568f2fbb90146469445.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0810.5517v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

On the freeze quantifier in Constraint LTL: Decidability and complexity

Stéphane Demri, Ranko Lazić, David Nowak
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
Constraint LTL, a generalisation of LTL over Presburger constraints, is often used as a formal language to specify the behavior of operational models with constraints.  ...  Many versions of freeze-free Constraint LTL are decidable over domains with qualitative predicates and our undecidability result actually establishes Sigma_1^1-completeness.  ...  The model-checking problem rests on D-automata which are constraints automata.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ic.2006.08.003">doi:10.1016/j.ic.2006.08.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6at65uubjbhk3c2gvqgxqwunam">fatcat:6at65uubjbhk3c2gvqgxqwunam</a> </span>
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When Model-Checking Freeze LTL over Counter Machines Becomes Decidable [chapter]

Stéphane Demri, Arnaud Sangnier
<span title="">2010</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We study the decidability status of model-checking freeze LTL over various subclasses of counter machines for which the reachability problem is known to be decidable (reversal-bounded counter machines,  ...  In freeze LTL, a register can store a counter value and at some future position an equality test can be done between a register and a counter value.  ...  We would like to thank the anonymous referees for their comments and suggestions on a preliminary version.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-12032-9_13">doi:10.1007/978-3-642-12032-9_13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xgdo6bdgrjdrzc5txqky7ctora">fatcat:xgdo6bdgrjdrzc5txqky7ctora</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120117160920/http://www.lsv.ens-cachan.fr/Publis/PAPERS/PDF/DS-fossacs10.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8b/9d/8b9d17cc787b026ac60456be5867651325f8de26.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-12032-9_13"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

LTL with the Freeze Quantifier and Register Automata [article]

Stephane Demri, Ranko Lazic
<span title="2008-04-03">2008</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
By translations from the logic to alternating automata with registers and then to faulty counter automata whose counters may erroneously increase at any time, and from faulty and error-free counter automata  ...  In particular, the logic with future-time operators and 1 register is decidable but not primitive recursive over finite data words.  ...  In [Demri et al. 2008] , decidability was obtained by replacing satisfiability with model checking data words generated by deterministic one-counter automata.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0610027v3">arXiv:cs/0610027v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xqrrprfolzgm3fav2xe7bqqoju">fatcat:xqrrprfolzgm3fav2xe7bqqoju</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-cs0610027/cs0610027.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c1/3c/c13c030bddfe46b36a076fc8a0c5e54e836f823b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0610027v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Temporal Logics on Words with Multiple Data Values [article]

Ahmet Kara, Thomas Schwentick, Thomas Zeume
<span title="2010-10-06">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
By reduction to the emptiness problem for data automata it is shown that this basic logic is decidable.  ...  It considers a basic logic which is a semantical fragment of the logic LTL^↓_1 of Demri and Lazic with operators for navigation into the future and the past.  ...  BD-LTL on infinite attributed words is decidable Over attributed ω-words BD-LTL remains decidable.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1010.1139v1">arXiv:1010.1139v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rea3c4nxdjga5euot2cr3mhbka">fatcat:rea3c4nxdjga5euot2cr3mhbka</a> </span>
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LTL with the freeze quantifier and register automata

Stéphane Demri, Ranko Lazić
<span title="2009-04-01">2009</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3kjjbv4edjbezl2w37ipy5lo5a" style="color: black;">ACM Transactions on Computational Logic</a> </i> &nbsp;
We investigate relative expressiveness and complexity of standard decision problems for LTL with the freeze quantifier (LTL ↓ ), 2-variable first-order logic (FO 2 ) over data words, and register automata  ...  We also prove that surprisingly, over infinite data words, LTL ↓ without the 'until' operator, as well as nonemptiness of one-way universal register automata, are undecidable even when there is only 1  ...  semi-structured data [21, 7, 3] , verifying timed systems [2, 1] , model checking constrained automata [8] , and verifying dynamic systems with resources [17] , quoting a few examples.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1507244.1507246">doi:10.1145/1507244.1507246</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s4pykrygdjdtrilfe7vsbvrg24">fatcat:s4pykrygdjdtrilfe7vsbvrg24</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170813162405/http://www.lsv.fr/Publis/PAPERS/PDF/DL-lics2006.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0b/3f/0b3f7a73e105b4d87e501d1d9b1f1f9ea061228c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1507244.1507246"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Automata and Logics for Words and Trees over an Infinite Alphabet [chapter]

Luc Segoufin
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
These models have been considered in the realm of semistructured data, timed automata and extended temporal logics.  ...  This paper survey several know results on automata and logics manipulating data words and data trees, the focus being on their relative expressive power and decidability.  ...  LTL ↓ 1 (X, U ) is decidable over data words. 2. LTL ↓ 2 (X, F ) is undecidable over data words. 3. LTL ↓ 1 (X, F, F −1 ) is undecidable over data words.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11874683_3">doi:10.1007/11874683_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wjiqqs7b5rhavluweikcda2l74">fatcat:wjiqqs7b5rhavluweikcda2l74</a> </span>
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Antichains: Alternative Algorithms for LTL Satisfiability and Model-Checking [chapter]

M. De Wulf, L. Doyen, N. Maquet, J. -F. Raskin
<span title="">2008</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Our algorithms do not construct nondeterministic automata from LTL formulas but work directly with alternating automata using efficient exploration techniques based on antichains.  ...  Introduction A model for an LTL formula over a set P of propositions is an infinite word w over the alphabet Σ = 2 P . An LTL formula φ defines a set of words is empty.  ...  LTL model-checking Our algorithm for LTL model-checking is based on forward exploration and semisymbolic representations.  ... 
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Extending nuXmv with Timed Transition Systems and Timed Temporal Properties [chapter]

Alessandro Cimatti, Alberto Griggio, Enrico Magnago, Marco Roveri, Stefano Tonetta
<span title="">2019</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this paper, we present a new version that supports timed systems and logics over continuous super-dense semantics.  ...  The results show that NUXMV is competitive with and in many cases performs better than state-of-the-art tools, especially on validity problems for MTL0,∞.  ...  Therefore, NUXMV now supports model checking of invariant, LTL and MTL 0,∞ properties over (symbolic) timed transition systems, as well as validity/satisfiability checking of LTL and MTL 0,∞ formulas.  ... 
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