scholarly journals An algorithmic approach for checking closure properties of temporal logic specifications and ω-regular languages

1998 ◽  
Vol 195 (2) ◽  
pp. 183-203 ◽  
Author(s):  
Doron Peled ◽  
Thomas Wilke ◽  
Pierre Wolper
Keyword(s):  
Temporal Logic ◽  
Regular Languages ◽  
Closure Properties ◽  
Algorithmic Approach

RESTARTING TILING AUTOMATA

2013 ◽  
Vol 24 (06) ◽  
pp. 863-878 ◽  
Author(s):  
DANIEL PRŮŠA ◽  
FRANTIŠEK MRÁZ
Keyword(s):  
Regular Languages ◽  
Two Dimensional ◽  
Scanning Strategy ◽  
Closure Properties ◽  
Computing Device ◽  
New Model ◽  
Picture Languages

We present a new model of a two-dimensional computing device called restarting tiling automaton. The automaton defines a set of tile-rewriting, weight-reducing rules and a scanning strategy by which a tile to rewrite is being searched. We investigate properties of the induced families of picture languages. Special attention is paid to picture languages that can be accepted independently of the scanning strategy. We show that this family strictly includes REC and exhibits similar closure properties. Moreover, we prove that its intersection with the set of one-row languages coincides with the regular languages.

FINITE STATE PROCESSES, Z-TEMPORAL LOGIC AND THE MONADIC THEORY OF THE INTEGERS

1992 ◽  
Vol 03 (03) ◽  
pp. 233-244 ◽  
Author(s):  
A. SAOUDI ◽  
D.E. MULLER ◽  
P.E. SCHUPP
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Second Order ◽  
Regular Languages ◽  
Infinite Words ◽  
First Order ◽  
Monadic Theory ◽  
Finite State ◽  
Temporal Formula

We introduce four classes of Z-regular grammars for generating bi-infinite words (i.e. Z-words) and prove that they generate exactly Z-regular languages. We extend the second order monadic theory of one successor to the set of the integers (i.e. Z) and give some characterizations of this theory in terms of Z-regular grammars and Z-regular languages. We prove that this theory is decidable and equivalent to the weak theory. We also extend the linear temporal logic to Z-temporal logic and then prove that each Z-temporal formula is equivalent to a first order monadic formula. We prove that the correctness problem for finite state processes is decidable.

UNWEIGHTED AND WEIGHTED HYPER-MINIMIZATION

2012 ◽  
Vol 23 (06) ◽  
pp. 1207-1225 ◽  
Author(s):  
ANDREAS MALETTI ◽  
DANIEL QUERNHEIM
Keyword(s):  
Finite Automata ◽  
Reduction Technique ◽  
Regular Languages ◽  
Minimization Algorithm ◽  
Compression Method ◽  
Closure Properties ◽  
State Reduction ◽  
Deterministic Finite Automata ◽  
Input Strings ◽  
Weighted Finite Automata

Hyper-minimization of deterministic finite automata (DFA) is a recently introduced state reduction technique that allows a finite change in the recognized language. A generalization of this lossy compression method to the weighted setting over semifields is presented, which allows the recognized weighted language to differ for finitely many input strings. First, the structure of hyper-minimal deterministic weighted finite automata is characterized in a similar way as in classical weighted minimization and unweighted hyper-minimization. Second, an efficient hyper-minimization algorithm, which runs in time [Formula: see text], is derived from this characterization. Third, the closure properties of canonical regular languages, which are languages recognized by hyper-minimal DFA, are investigated. Finally, some recent results in the area of hyper-minimization are recalled.

scholarly journals On the Satisfiability and Model Checking for one Parameterized Extension of Linear-time Temporal Logic

2021 ◽  
Vol 28 (4) ◽  
pp. 356-371
Author(s):  
Anton Romanovich Gnatenko ◽  
Vladimir Anatolyevich Zakharov
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Linear Time ◽  
Complete Solution ◽  
Reactive Systems ◽  
Expressive Power ◽  
Regular Languages ◽  
Specification Languages ◽  
Temporal Logics ◽  
Emptiness Problem

Sequential reactive systems are computer programs or hardware devices which process the flows of input data or control signals and output the streams of instructions or responses. When designing such systems one needs formal specification languages capable of expressing the relationships between the input and output flows. Previously, we introduced a family of such specification languages based on temporal logics $LTL$, $CTL$ and $CTL^*$ combined with regular languages. A characteristic feature of these new extensions of conventional temporal logics is that temporal operators and basic predicates are parameterized by regular languages. In our early papers, we estimated the expressive power of the new temporal logic $Reg$-$LTL$ and introduced a model checking algorithm for $Reg$-$LTL$, $Reg$-$CTL$, and $Reg$-$CTL^*$. The main issue which still remains unclear is the complexity of decision problems for these logics. In the paper, we give a complete solution to satisfiability checking and model checking problems for $Reg$-$LTL$ and prove that both problems are Pspace-complete. The computational hardness of the problems under consideration is easily proved by reducing to them the intersection emptyness problem for the families of regular languages. The main result of the paper is an algorithm for reducing the satisfiability of checking $Reg$-$LTL$ formulas to the emptiness problem for Buchi automata of relatively small size and a description of a technique that allows one to check the emptiness of the obtained automata within space polynomial of the size of input formulas.

scholarly journals Extended Temporal Logic on Finite Words and Wreath Product of Monoids with Distinguished Generators

2002 ◽  
Vol 9 (47) ◽  
Author(s):  
Zoltán Ésik
Keyword(s):  
Temporal Logic ◽  
Wreath Product ◽  
Expressive Power ◽  
Regular Languages ◽  
Modal Operator

We associate a modal operator with each language belonging to a given class of regular languages and use the (reverse) wreath product of monoids with distinguished generators to characterize the expressive power of the resulting logic.

Two-Sided Strictly Locally Testable Languages

2021 ◽  
Vol 180 (1-2) ◽  
pp. 29-51
Author(s):  
Markus Holzer ◽  
Martin Kutrib ◽  
Friedrich Otto
Keyword(s):  
Binary Relation ◽  
Regular Languages ◽  
Decision Problems ◽  
Closure Properties ◽  
Positive Data ◽  
Proper Subclass ◽  
Testable Language ◽  
Even Linear Languages

A two-sided extension of strictly locally testable languages is presented. In order to determine membership within a two-sided strictly locally testable language, the input must be scanned from both ends simultaneously, whereby it is synchronously checked that the factors read are correlated with respect to a given binary relation. The class of two-sided strictly locally testable languages is shown to be a proper subclass of the even linear languages that is incomparable to the regular languages with respect to inclusion. Furthermore, closure properties of the class of two-sided strictly locally testable languages and decision problems are studied. Finally, it is shown that two-sided strictly k-testable languages are learnable in the limit from positive data.

Sign in / Sign up

Export Citation Format

Share Document