scholarly journals Regular Languages Definable by Lindström Quantifiers

2003 ◽  
Vol 10 (28) ◽  
Author(s):  
Zoltán Ésik ◽  
Kim G. Larsen
Keyword(s):  
Semidirect Product ◽  
Expressive Power ◽  
Regular Languages ◽  
Finite Monoids

In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.

Regular Languages Definable by Lindström Quantifiers (Preliminary Version)

2002 ◽  
Vol 9 (20) ◽  
Author(s):  
Zoltán Ésik ◽  
Kim G. Larsen
Keyword(s):  
Semidirect Product ◽  
Expressive Power ◽  
Regular Languages ◽  
Finite Monoid ◽  
Preliminary Version

In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoid-generator pairs. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.<br /><br />Superseded by BRICS-RS-03-28.

scholarly journals Positive Neural Networks in Discrete Time Implement Monotone-Regular Behaviors

2015 ◽  
Vol 27 (12) ◽  
pp. 2623-2660 ◽  
Author(s):  
Tom J. Ameloot ◽  
Jan Van den Bussche
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Discrete Time ◽  
Expressive Power ◽  
Regular Languages ◽  
Regular Behavior ◽  
Multiple Input

We study the expressive power of positive neural networks. The model uses positive connection weights and multiple input neurons. Different behaviors can be expressed by varying the connection weights. We show that in discrete time and in the absence of noise, the class of positive neural networks captures the so-called monotone-regular behaviors, which are based on regular languages. A finer picture emerges if one takes into account the delay by which a monotone-regular behavior is implemented. Each monotone-regular behavior can be implemented by a positive neural network with a delay of one time unit. Some monotone-regular behaviors can be implemented with zero delay. And, interestingly, some simple monotone-regular behaviors cannot be implemented with zero delay.

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.

scholarly journals ON FREE SPECTRA OF A CLASS OF FINITE INVERSE MONOIDS

2012 ◽  
Vol 93 (3) ◽  
pp. 225-237
Author(s):  
IGOR DOLINKA
Keyword(s):  
Semidirect Product ◽  
Natural Order ◽  
Inverse Monoid ◽  
Left Action ◽  
Inverse Monoids ◽  
Group Of Units ◽  
Finite Monoids ◽  
Free Spectrum ◽  
Free Spectra

AbstractFor a finite Clifford inverse algebra $A$, with natural order meet-semilattice ${Y}_{A} $ and group of units ${G}_{A} $, we show that the inverse monoid obtained as the semidirect product ${ Y}_{A}^{1} {\mathop{\ast }\nolimits}_{\rho } {G}_{A} $ has a log-polynomial free spectrum whenever $\rho $ is a term-expressible left action of ${G}_{A} $ on ${Y}_{A} $ and all subgroups of $A$ are nilpotent. This yields a number of examples of finite inverse monoids satisfying the Seif conjecture on finite monoids whose free spectra are not doubly exponential.

scholarly journals On the Expressive Power of Stateless Ordered Restart-Delete Automata

2021 ◽  
Author(s):  
Friedrich Otto
Keyword(s):  
Expressive Power ◽  
Single Letter ◽  
Regular Languages ◽  
Descriptional Complexity ◽  
Context Free

AbstractStateless ordered restart-delete automata (stl-ORD-automata) are studied. These are obtained from the stateless ordered restarting automata (stl-ORWW-automata) by introducing an additional restart-delete operation, which, based on the surrounding context, deletes a single letter. While the stl-ORWW-automata accept the regular languages, we show that the swift stl-ORD-automata yield a characterization for the class of context-free languages. Here a stl-ORD-automaton is called swift if it can move its window to any position after performing a restart. We also study the descriptional complexity of swift stl-ORD-automata and relate them to limited context restarting automata.

THE GLOBALS OF SOME SUBPSEUDOVARIETIES OF $\mathsf{DA}$

2004 ◽  
Vol 14 (05n06) ◽  
pp. 525-549 ◽  
Author(s):  
J. ALMEIDA ◽  
A. ESCADA
Keyword(s):  
Word Problem ◽  
Semidirect Product ◽  
Product Formula ◽  
Finite Monoids

Let [Formula: see text] be the pseudovariety of all finite monoids whose principal right ideals have a unique generator, let [Formula: see text] be its dual, and let [Formula: see text]. Using the word problem for free pro-[Formula: see text] monoids, it is shown that the bilateral semidirect product [Formula: see text] is local, where [Formula: see text] denotes the pseudovariety of all finite semilattices. The global of the pseudovariety where [Formula: see text] is also computed and it is shown that this join is not local.

Learning Regular Languages from Positive Evidence

1998 ◽  
Author(s):  
Laura Firoiu ◽  
Tim Oates ◽  
Paul R. Cohen
Keyword(s):  
Regular Languages ◽  
Positive Evidence

Recursive generation in language

2017 ◽  
Author(s):  
David J. Lobina
Keyword(s):  
Mathematical Logic ◽  
Production System ◽  
General Property ◽  
Recent Literature ◽  
Expressive Power ◽  
The Self ◽  
Recursive Structure ◽  
Embedded Structures ◽  
Mechanical Procedure ◽  
The 1950S

The introduction of recursion into linguistics was the result of applying some of the results of mathematical logic to the study of language. In particular, recursion was introduced in the 1950s as a general property of the mechanical procedure underlying the grammar, in order to account for language’s discrete infinity and expressive power—in the 1950s, this mechanical procedure was a production system, whereas more recently, of course, it is the set-operator merge. Unfortunately, the recent literature has confused the general recursive property of a grammar with specific instances of (recursive) rules/operations within a grammar; more worryingly still, there has been a general conflation of these recursive rules with some of the self-embedded structures these rules can generate, adding to the confusion. The conflation is manifold but always fallacious. Moreover, language manifests a much more generally recursive structure than is usually recognized: bundles of the universal (Specifier)-Head-Complement(s) geometry.

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