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Improving Automata Generation for Linear Temporal Logic by Considering the Automaton Hierarchy
[chapter]

2001
*
Lecture Notes in Computer Science
*

Using

doi:10.1007/3-540-45653-8_3
fatcat:3jofakfytzcqdfazmebemir264
*the*well-known*automaton**hierarchy*, we show that our*improvements*are complete. ... We present new algorithms to translate*linear*time*temporal**logic*(LTL) formulas with past operators to equivalent ω-*automata*. ... We therefore claim that our translations outperform state-of-*the*-art symbolic model checking tools*for*LTL. ...##
###
Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis

2010
*
Electronic Proceedings in Theoretical Computer Science
*

*The*classic approaches to synthesize a reactive system from a

*linear*

*temporal*

*logic*(LTL) specification first translate

*the*given LTL formula to an equivalent omega-

*automaton*and then compute a winning ... In particular, we exploit (1)

*the*

*temporal*

*logic*

*hierarchy*that corresponds to

*the*well-known

*automata*

*hierarchy*consisting of safety, liveness, Buechi, and co-Buechi

*automata*as well as their boolean ...

*The*

*temporal*

*logic*

*hierarchy*[5, 25] has been developed in correspondence to

*the*ω-

*automata*

*hierarchy*[14] that has been inspired

*by*

*the*Borel

*hierarchy*known from descriptive set theory. ...

##
###
Relating Hierarchy of Temporal Properties to Model Checking
[chapter]

2003
*
Lecture Notes in Computer Science
*

Our contribution Our aim is to classify

doi:10.1007/978-3-540-45138-9_26
fatcat:zllmtn2c7rekzgtde7xj5z4l2m
*temporal*properties specifiable*by**linear**temporal**logic*formulas with respect to*the*complexity of their verification. ...*Linear**Temporal**Logic*View In this section we characterise*the**hierarchy*of properties through a new*hierarchy*of LTL formulas based on an alternation depth. ...##
###
A LTL Fragment for GR(1)-Synthesis

2011
*
Electronic Proceedings in Theoretical Computer Science
*

*The*idea of automatic synthesis of reactive programs starting from

*temporal*

*logic*(LTL) specifications is quite old, but was commonly thought to be infeasible due to

*the*known double exponential complexity ... To this end, manually written deterministic omega-

*automata*having GR(1) conditions were used instead of

*the*original LTL specifications. ... Preliminaries

*Linear*

*Temporal*

*Logic*LTL

*For*a given set of Boolean variables V, we define

*the*set of LTL formulas

*by*

*the*following recursive definition: Definition 1 (Syntax of

*Linear*

*Temporal*

*Logic*...

##
###
Page 6287 of Mathematical Reviews Vol. , Issue 2003h
[page]

2003
*
Mathematical Reviews
*

|Schneider, Kai] (D-K LRH-FT; Karlsruhe)

*Improving**automata**generation**for**linear**temporal**logic**by**considering**the**automaton**hierarchy*. ... Using*the*well-known*automata**hierarchy*, we show that our*improvements*are complete. ...##
###
Almost Linear Büchi Automata

2009
*
Electronic Proceedings in Theoretical Computer Science
*

We introduce a new fragment of

doi:10.4204/eptcs.8.2
fatcat:zmhywtopizdlfj3cr5xg3inmha
*Linear**temporal**logic*(LTL) called LIO and a new class of Buechi*automata*(BA) called Almost*linear*Buechi*automata*(ALBA). ... As we expect applications of ALBA in model checking, we compare*the*expressiveness of ALBA with other classes of Buechi*automata*studied in this context and we indicate possible applications. ...*Linear**temporal**logic*(LTL)*The*syntax of*Linear**Temporal**Logic*(LTL) [11] is defined as follows ϕ ::= tt | a | ¬ϕ | ϕ ∨ ϕ | ϕ ∧ ϕ | Fϕ | Gϕ | Xϕ | ϕ U ϕ, where tt stands*for*true, a ranges over a countable ...##
###
Almost linear Büchi automata

2012
*
Mathematical Structures in Computer Science
*

We introduce a new fragment of

doi:10.1017/s0960129511000399
fatcat:ta2qac3evzajngshn7m23chymi
*Linear**temporal**logic*(LTL) called LIO and a new class of Büchi*automata*(BA) called Almost*linear*Büchi*automata*(ALBA). ... As we expect applications of ALBA in model checking, we compare*the*expressiveness of ALBA with other classes of Büchi*automata*studied in this context and we indicate possible applications. ...*Linear**temporal**logic*(LTL)*The*syntax of*Linear**Temporal**Logic*(LTL) [11] is defined as follows ϕ ::= tt | a | ¬ϕ | ϕ ∨ ϕ | ϕ ∧ ϕ | Fϕ | Gϕ | Xϕ | ϕ U ϕ, where tt stands*for*true, a ranges over a countable ...##
###
Stutter-Invariant Languages, ω-Automata, and Temporal Logic
[chapter]

1999
*
Lecture Notes in Computer Science
*

*Temporal*

*logic*and ω-

*automata*are two of

*the*common frameworks

*for*specifying properties of reactive systems in modern verification tools. ... We will observe a simple variant of

*linear*time propositional

*temporal*

*logic*(LTL)

*for*expressing exactly

*the*stutter-invariant ω-regular languages. ... Conclusions We have provided a simple

*temporal*

*logic*, SI-EQLTL,

*for*expressing

*the*stutterinvariant ω-regular languages. ...

##
###
Page 443 of Mathematical Reviews Vol. , Issue 92a
[page]

1992
*
Mathematical Reviews
*

Summary: “In order to enhance

*the*readability and to simplify*the*verification of*temporal**logic*programs in*the*XYZ system, we propose a structured*temporal**logic*language called XYZ/SE, based on XYZ/ ... Summary: “*Consider*a cellular*automaton*defined on Z where each lattice site may take on one of N values, referred to as colors. ...##
###
Relating word and tree automata

2006
*
Annals of Pure and Applied Logic
*

We

doi:10.1016/j.apal.2005.06.009
fatcat:jscbgtaccbddjmg6qu2zy7irzq
*consider*tree*automata*that recognize derived languages.*For*a word language L,*the*derived language of L, denoted L , is*the*set of all trees all of whose paths are in L. ... Our main result shows that L is recognizable*by*a nondeterministic Büchi word*automaton*but not*by*a deterministic Büchi word*automaton*iff L is recognizable*by*a Rabin tree*automaton*and not*by*a Büchi ...*Linear**temporal**logic*formulas correspond to word*automata*and branching*temporal**logic*formulas correspond to tree*automata*. ...##
###
Product Interval Automata: A Subclass of Timed Automata
[chapter]

1999
*
Lecture Notes in Computer Science
*

Automated analysis of timed

doi:10.1007/3-540-46691-6_5
fatcat:drc3suuptfgzbi7cwjkxey5fo4
*automata*relies on*the*construction of a nite quotient of*the*in nite space of clock valuations. ... Over*the*years,*the*formalism has been extensively studied leading to many results establishing connections to circuits and*logic*, and much progress has been made in developing veri cation algorithms, ... Many thanks to them, and to Salvatore La Torre*for*comments on this survey. ...##
###
Timed Automata
[chapter]

1999
*
Lecture Notes in Computer Science
*

Automated analysis of timed

doi:10.1007/3-540-48683-6_3
fatcat:krziony2hzgj5ploa37xa5jfcy
*automata*relies on*the*construction of a finite quotient of*the*infinite space of clock valuations. ... Over*the*years,*the*formalism has been extensively studied leading to many results establishing connections to circuits and*logic*, and much progress has been made in developing verification algorithms, ... Many thanks to them, and to Salvatore La Torre*for*comments on this survey. ...##
###
Reservoir Computing using Cellular Automata
[article]

2014
*
arXiv
*
pre-print

Input is randomly projected onto

arXiv:1410.0162v1
fatcat:phm4z7o45fdnnkmm6qf5oakosa
*the*initial conditions of*automaton*cells and nonlinear computation is performed on*the*input via application of a rule in*the**automaton**for*a period of time. ...*The*evolution of*the**automaton*creates a space-time volume of*the**automaton*state space, and it is used as*the*reservoir. ...*The*input in a complex task is*generated**by*multiple different processes,*for*which*the*dynamics and spatio-*temporal*correlations might be very different. ...##
###
Real Time Temporal Logic: Past, Present, Future
[chapter]

2005
*
Lecture Notes in Computer Science
*

We start

doi:10.1007/11603009_2
fatcat:xyskxkorjbcvncuu7sob3rjyb4
*by*giving a constructive proof of*the*folk theorem stating that timed languages specified*by**the*past fragment of MITL, can be accepted*by*deterministic timed*automata*. ... This paper attempts to*improve*our understanding of timed languages and their relation to timed*automata*. ... Lakhnech and from comments made*by*D. Fisman, T. Henzinger and anonymous referees. ...##
###
Weak Automata for the Linear Time μ-Calculus
[chapter]

2005
*
Lecture Notes in Computer Science
*

We write [[α]]

doi:10.1007/978-3-540-30579-8_18
fatcat:ixe5hogilnhq5fjy7iskzhuvjm
*for**the*language defined*by*α. ... This yields a normal form*for*these formulas, in fact showing that*the**linear*time alternation*hierarchy*collapses at level 0 and not just at level 1 as known so far. ... But*the*translation back from weak alternating parity*automata*into formulas of*the**linear*time µ-calculus even*improves*this:*the*µTL alternation*hierarchy*indeed collapses at level 0. ...
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