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Regular Solutions of Language Inequalities and Well Quasi-orders
[chapter]
2004
Lecture Notes in Computer Science
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By means of constructing suitable well quasi-orders of free monoids we prove that all maximal solutions of certain systems of language inequalities are regular. ...
In a similar manner we also demonstrate that the largest solution of the inequality XK ⊆ LX is regular provided the language L is regular. ...
I also appreciate Jean-Éric Pin's suggestion to investigate a connection between decomposition quasi-orders and unavoidability of sets of words, which allowed to simplify the proof of Theorem 10. ...
doi:10.1007/978-3-540-27836-8_73
fatcat:7fqab3nbsjfbbkunclh7h4f23q
Regular solutions of language inequalities and well quasi-orders
2005
Theoretical Computer Science
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By means of constructing suitable well quasi-orders of free monoids we prove that all maximal solutions of certain systems of language inequalities are regular. ...
In a similar manner we also demonstrate that the largest solution of the inequality XK ⊆ LX is regular provided the language L is regular. ...
I also appreciate Jean-Éric Pin's suggestion to investigate a connection between decomposition quasi-orders and unavoidability of sets of words, which allowed to simplify the proof of Theorem 10. ...
doi:10.1016/j.tcs.2005.09.018
fatcat:cgc4ua7hyjgxzp2zdikr35jbtu
How to Prove that a Language Is Regular or Star-Free?
[chapter]
2020
Lecture Notes in Computer Science
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Most books of automata theory [9, 23, 29, 45, 49] offer exercises on regular languages, including some difficult ones. ...
This survey article presents some standard and less standard methods used to prove that a language is regular or star-free. ...
Rewriting Systems and Well Quasi-orders Rewriting systems and well quasi-orders are two powerful methods to prove the regularity of a language. We follow the terminology of Otto's survey [37] . ...
doi:10.1007/978-3-030-40608-0_5
fatcat:mzoyw7mckzgxnhyggsxiq4bhoa
On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations
2010
Fuzzy sets and systems (Print)
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In this paper we study systems of fuzzy relation inequalities and equations of the form U where U is an unknown and V i (i ∈ I) are given fuzzy relations, the dual systems , and certain special types of ...
For each weakly linear system, with a complete residuated lattice as the underlying structure of truth values, we prove the existence of the greatest solution, and we provide an algorithm for computing ...
Strongly right regular fuzzy quasi-orders and fuzzy equivalences with respect to {δ A x } x∈X and Q τ , as well as strongly left regular fuzzy quasi-orders and fuzzy equivalences with respect to {δ A x ...
doi:10.1016/j.fss.2010.08.002
fatcat:rslsnqltffhgxkpkzc2d5xoija
Well quasi-orders arising from finite ordered semigroups
[article]
2022
arXiv
pre-print
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The question is which of these homomorphisms induce a well quasi-order on the set of all words. ...
We show that this problem is decidable and the answer does not depend on the homomorphism, but it is a property of the ordered semigroup. ...
On the other hand, in [8] , the wqo was applied to prove regularity of maximal solutions of very general language equations and inequalities (see also [12] ). ...
arXiv:2203.06535v1
fatcat:shfwul6khbcmvjdtwrwnfnipca
On Free ω-Continuous and Regular Ordered Algebras
[article]
2019
arXiv
pre-print
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For example, we show that if E is a set of inequalities between finite Σ-terms, and if V_ω and V_reg denote the varieties of all ω-continuous ordered Σ-algebras and regular ordered Σ-algebras satisfying ...
This is a special case of a more general construction that applies to any quasi-regular family. ...
Thanks to the anonymous referees for their careful reading and valuable suggestions that greatly improved the presentation. This research was supported in part by NSF grant AiTF-1637532. ...
arXiv:1612.02106v5
fatcat:rfhfsu2surfpvee5v6dcptwfee
On Free ω-Continuous and Regular Ordered Algebras
2016
Logical Methods in Computer Science
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For example, we show that if E is a set of inequalities between finite Σ-terms, and if Vω and Vreg denote the varieties of all ω-continuous ordered Σ-algebras and regular ordered Σ-algebras satisfying ...
This is a special case of a more general construction that applies to any quasi-regular family. ...
Thanks to the anonymous referees for their careful reading and valuable suggestions that greatly improved the presentation. This research was supported in part by NSF grant AiTF-1637532. ...
doi:10.23638/lmcs-15(4:4)2019
fatcat:yjrhz65365awhhqu32alc2f2oe
Existential questions in (relatively) hyperbolic groups and Finding relative hyperbolic structures
[article]
2008
arXiv
pre-print
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We show that the satisfiability of systems of equations and inequations is decidable in these groups. ...
This arXived paper has two independant parts, that are improved and corrected versions of different parts of a single paper once named "On equations in relatively hyperbolic groups". ...
With the above assumptions, given arbitrary orders in generating sets of each P i , any gnr language is normalized regular. Consider a language L in IL(gnr), and an associated gnr • -automaton A. ...
arXiv:math/0505345v4
fatcat:62ntyypbnzbqtct64d2vizucem
Weakly linear systems of fuzzy relation inequalities and their applications: A brief survey
2012
Filomat
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Weakly linear systems of fuzzy relation inequalities and equations have recently emerged from research in the theory of fuzzy automata. ...
From the general aspect of the theory of fuzzy relation equations and inequalities homogeneous and heterogeneous weakly linear systems have been discussed in two recent papers. ...
, i.e., the greatest right regular, left regular and regular fuzzy quasi orders contained in M (cf. ...
doi:10.2298/fil1202207i
fatcat:4ypn6ph435eqhck4sfynwdlili
Page 7072 of Mathematical Reviews Vol. , Issue 2003i
[page]
2003
Mathematical Reviews
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These results imply, in particular, that the problem of incrementally generating all minimal integer solutions to a monotone system of linear inequalities can be done in quasi-polynomial time.” ...
Summary: “We consider the problem of enumerating all minimal integer solutions of a monotone system of linear inequalities. ...
Information Inequalities for Joint Distributions, With Interpretations and Applications
2010
IEEE Transactions on Information Theory
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These inequalities generalize Shannon's chain rule for entropy as well as inequalities of Han, Fujishige, and Shearer. A duality between the upper and lower bounds for joint entropy is developed. ...
The new inequalities are applied to obtain new results in combinatorics, such as bounds on the number of independent sets in an arbitrary graph and the number of zero-error source-channel codes, as well ...
Barron for many useful discussions, and for the indirect influence of his joint work [33] with M. Madiman on entropy power inequalities. ...
doi:10.1109/tit.2010.2046253
fatcat:ogefdqsy65c7dipfkzzvtuawwy
The complexity of solution sets to equations in hyperbolic groups
[article]
2020
arXiv
pre-print
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We show that the full set of solutions to systems of equations and inequations in a hyperbolic group, as shortlex geodesic words (or any regular set of quasigeodesic normal forms), is an EDT0L language ...
Furthermore, in the presence of quasi-isometrically embeddable rational constraints, we show that the full set of solutions to systems of equations in a hyperbolic group remains EDT0L. ...
It is well known (see for example [40, Theorem V.1.7] ) that the class of ET0L languages is closed under homomorphism, inverse homomorphism, finite union, and intersection with regular languages (a full ...
arXiv:2001.09591v4
fatcat:7ouhk4mlqrhh5g6ufyh2ggc6ka
Dual Space of a Lattice as the Completion of a Pervin Space
[chapter]
2017
Lecture Notes in Computer Science
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We assume the reader is familiar with basic topology on the one hand and finite automata theory on the other hand. No proofs are given in this extended abstract. ...
Künzi and Marcel Erné were greatly appreciated. ...
Acknowledgements I would like to thank Mai Gehrke and Serge Grigorieff for many fruitful discussions on Pervin spaces. ...
doi:10.1007/978-3-319-57418-9_2
fatcat:blqgjzhya5gc3cmecdd2dtgoxy
Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models
2015
Applied Mechanics and Materials
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Finally, the link with the classical dynamic Griffith theory and with the original quasi-static model as well as various dynamic fracture phenomena are illustrated by representative numerical examples ...
The dynamic evolution problem for a general class of such damage models is formulated as a variational inequality involving the action integral of a generalized Lagrangian and its physical interpretation ...
From Fig. 5 (left) we see that dynamic solution coincides well with the quasi-static solution, showing that G dyn ≈ G stat ≈ (G c ) eff during the propagation phase. ...
doi:10.4028/www.scientific.net/amm.784.334
fatcat:bihxbgtpefcyjl4r7hthosnu7m
SOLVABILITY OF BOUNDARY VALUE PROBLEMS WITH NON-LOCAL CONDITIONS FOR MULTIDIMENSIONAL HYPERBOLIC EQUATIONS
2020
Izvestiâ Nacionalʹnoj akademii nauk Respubliki Kazahstan. Seriâ fiziko-matematičeskaâ
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This equation is an ordinary second-order hyperbolic equation, and the solvability of natural boundary value and initial-boundary value problems for it is well studied [24] [25] [26] . ...
The aim of the work is to study the solvability in classes of regular solutions of a new boundary value problem for the equation ∆ , , , , ∈ . ...
or in any other language, including electronically without the written consent of the copyrightholder. ...
doi:10.32014/2020.2518-1726.21
fatcat:jhfw5gfy3bf7bohwuzlfkkrhne
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