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Extended Temporal Logic Revisited [chapter]

Orna Kupferman, Nir Piterman, Moshe Y. Vardi
2001 Lecture Notes in Computer Science  
The rich structure of two-way alternating automata makes ETL © a very powerful and convenient logic.  ...  Two-way automata can traverse the input word back and forth and they are exponentially more succinct than one-way automata.  ...  Two-way alternating automata A 2-way alternating automaton is 3 R¨ !  ... 
doi:10.1007/3-540-44685-0_35 fatcat:nrex2uqzpvbq5fq3ejmtcbptoa

Regular Linear-Time Temporal Logic

Martin Leucker, Cesar Sanchez
2010 2010 17th International Symposium on Temporal Representation and Reasoning  
Unlike LTL, RLTL can define all ω-regular languages and unlike previous approaches, RLTL is defined with an algebraic signature, does not depend on fix-points in its syntax, and provides past operators  ...  The satisfiability and model checking problems for RLTL are PSPACE-complete, which is optimal for extensions of LTL.  ...  The problems of satisfiability and model checking are PSPACEcomplete [6] for LTL with and without past operators.  ... 
doi:10.1109/time.2010.29 dblp:conf/time/LeuckerS10 fatcat:qmbnjwevg5gglpbctmoid6ztje

Regular Linear Temporal Logic with Past [chapter]

César Sánchez, Martin Leucker
2010 Lecture Notes in Computer Science  
This paper upgrades Regular Linear Temporal Logic (RLTL) with past operators and complementation.  ...  This result is shown using a novel linear size translation of RLTL expressions into 2-way alternating parity automata on words.  ...  We wish to thank the anonymous reviewers for their helpful comments and suggestions.  ... 
doi:10.1007/978-3-642-11319-2_22 fatcat:r5atariepjdctdw4xo3xztp5la

GOAL for Games, Omega-Automata, and Logics [chapter]

Ming-Hsien Tsai, Yih-Kuen Tsay, Yu-Shiang Hwang
2013 Lecture Notes in Computer Science  
The new features include game solving, manipulation of two-way alternating automata, translation of ACTL formulae and ω-regular expressions, test of language star-freeness, classification of ω-regular  ...  The enhancements provide more automata conversion, complementation, simplification, and testing algorithms, translation of full QPTL formulae, and better automata navigation with more layout algorithms  ...  We thank Jinn-Shu Chang and Yi-Wen Chang for helping with the implementations of some algorithms.  ... 
doi:10.1007/978-3-642-39799-8_62 fatcat:4xi3csp63fgbhn736yrrhzc3we

On the Translation of Automata to Linear Temporal Logic [article]

Udi Boker, Karoliina Lehtinen, Salomon Sickert
2022 arXiv   pre-print
Our first contribution consists of tight bounds for LTL over a unary alphabet: alternating, nondeterministic and deterministic automata can be exactly exponentially, quadratically and linearly more succinct  ...  While the complexity of translating future linear temporal logic (LTL) into automata on infinite words is well-understood, the size increase involved in turning automata back to LTL is not.  ...  We thank Moshe Vardi and Orna Kupferman for suggesting studying the succinctness gap between semantic and syntactic safe formulas, and Miko laj Bojańczyk for answering our questions on algebraic automata  ... 
arXiv:2201.10267v1 fatcat:bbd7ejst6fe6nnkcczbw77zmme

Constructing Büchi Automata from Linear Temporal Logic Using Simulation Relations for Alternating Büchi Automata [chapter]

Carsten Fritz
2003 Lecture Notes in Computer Science  
), our procedure computes simulation relations for alternating Büchi automata in an early stage and uses them in an onthe-fly fashion.  ...  Our procedure is based on simulation relations for alternating Büchi automata.  ...  Acknowledgments Thanks to Björn Teegen who implemented LTL → NBA's parser for the LTL formulas, the web interface, and the interface to the dot program.  ... 
doi:10.1007/3-540-45089-0_5 fatcat:peh4y2e5gfg3ppcofwzhl54pha

Bounded Model Checking for Weak Alternating Büchi Automata [chapter]

Keijo Heljanko, Tommi Junttila, Misa Keinänen, Martin Lange, Timo Latvala
2006 Lecture Notes in Computer Science  
We present an incremental bounded model checking encoding into propositional satisfiability where the property specification is expressed as a weak alternating Büchi automaton (WABA).  ...  encoding is linear in the specification, or, more exactly O(|I| + k · |T | + k · |δ|), where |I| is the size of the initial state predicate, k is the bound, |T | is the size of the transition relation, and  ...  Roveri, and the rest of the NuSMV team for assistance and providing us with a development version of NuSMV.  ... 
doi:10.1007/11817963_12 fatcat:auy4iqgjrbay3erq77md7r76i4

Once and for all

Orna Kupferman, Amir Pnueli, Moshe Y. Vardi
2012 Journal of computer and system sciences (Print)  
Two possible views regarding the nature of past in a branching-time model induce two different such extensions.  ...  It has long been known that past-time operators add no expressive power to linear temporal logics. In this paper, we consider the extension of branching temporal logics with past-time operators.  ...  In order to handle linear past, we need an extension of symmetric alternating automata to two-way automata [31] .  ... 
doi:10.1016/j.jcss.2011.08.006 fatcat:tk3kr3kx3veyhezicrixui226i

The Planning Spectrum - One, Two, Three, Infinity

M. Pistore, M. Y. Vardi
2007 The Journal of Artificial Intelligence Research  
We show that only eight of these combinations of path quantifiers are relevant, corresponding to an alternation of the quantifiers of length one (A and E), two (AE and EA), three (AEA and EAE), and infinity  ...  In this paper we explore alternative interpretations of an LTL formula that are between these extreme cases.  ...  We would like to thank Erich Grädel for his comments on the reduction of -LTL formulas to CTL* formulas.  ... 
doi:10.1613/jair.1909 fatcat:7y6cstro4nb6bhybcnsijqpyk4

LTL with the Freeze Quantifier and Register Automata [article]

Stephane Demri, Ranko Lazic
2008 arXiv   pre-print
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.  ...  ACKNOWLEDGMENTS We are grateful to Claire David, Massimo Franceschet, Marcin Jurdziński, Anca Muscholl, David Nowak, Joël Ouaknine, Philippe Schnoebelen and Luc Segoufin for helpful discussions.  ... 
arXiv:cs/0610027v3 fatcat:xqrrprfolzgm3fav2xe7bqqoju

A Verified and Compositional Translation of LTL to Deterministic Rabin Automata

Julian Brunner, Benedikt Seidl, Salomon Sickert, Michael Wagner
2019 International Conference on Interactive Theorem Proving  
generic, executable, and expressive automata library providing necessary operations on automata to re-combine the "simple" languages; third, we instantiate this generic theory to obtain a construction  ...  We present a formalisation of the unified translation approach from linear temporal logic (LTL) to ω-automata from [19] .  ...  Further, the translation proposed by [22] , which translates LTL via very-weak alternating automata to NBAs, has been formalised by [25] in HOL4.  ... 
doi:10.4230/lipics.itp.2019.11 dblp:conf/itp/0001SS19 fatcat:zhsmqsspyfcd3f4uggptl3t7le

Alternation Elimination for Automata over Nested Words [chapter]

Christian Dax, Felix Klaedtke
2011 Lecture Notes in Computer Science  
With these alternation-elimination constructions at hand, we straightforwardly obtain translations from various temporal logics over nested words from the literature like CaRet and µNWTL, and extensions  ...  The scheme generalizes our alternation-elimination scheme for word automata and the presented complementation constructions generalize existing complementation constructions for word automata.  ...  (i) If A is (eventually) W -way then R is (eventually) W -way. (ii) If A is (very) weak then R is (very) weak.  ... 
doi:10.1007/978-3-642-19805-2_12 fatcat:ogzkdrnmlneb5nz2jyl33uyoiu

Model Checking Linear Properties of Prefix-Recognizable Systems [chapter]

Orna Kupferman, Nir Piterman, Moshe Y. Vardi
2002 Lecture Notes in Computer Science  
of one-way alternating weak automata on infinite words, which was studied in [KVW00].  ...  Büchi path automata is EXPTIME-complete, and the membership problem for two-way alternating Büchi automata is also EXPTIME-complete .  ...  We also consider weak alternating automata.  ... 
doi:10.1007/3-540-45657-0_31 fatcat:b72iabdq3nc6jdg2tjxffglacy

Efficient Model Checking of Safety Properties [chapter]

Timo Latvala
2003 Lecture Notes in Computer Science  
Our other contribution is an efficient algorithm for translating LTL safety properties to finite automata.  ...  This work discusses the theoretical and some of the practical issues related to model checking LTL properties.  ...  The financial support of Helsinki Graduate School in Computer Science and Engineering, the Academy of Finland (project 47754), the Wihuri Foundation and Tekniikan Edistämissäätiö (Foundation for Technology  ... 
doi:10.1007/3-540-44829-2_5 fatcat:zlkczcjjdfeijoekb66ohrtpe4

A HOL Conversion for Translating Linear Time Temporal Logic to ω-Automata [chapter]

Klaus Schneider, Dirk W. Hoffmann
1999 Lecture Notes in Computer Science  
We present an embedding of linear time temporal logic LTL in HOL together with an elegant translation of LTL formulas into equivalent ω-automata.  ...  The translation is completely implemented by HOL rules and is therefore safe. Its implementation is mainly based on preproven theorems such that the conversion works very efficiently.  ...  An elegant way for translating LTL into ω-automata by means of alternating ωautomata has been presented in [37] .  ... 
doi:10.1007/3-540-48256-3_17 fatcat:t56koncqhrhtfa62ntmi5micri
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