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Page 3208 of Mathematical Reviews Vol. , Issue 98E
[page]

1998
*
Mathematical Reviews
*

{For the entire collection see MR 98d:68015.}
98e:68142 68Q45 20M35 68Q70
Kari, Lila (3-WON; London, ON);
Theirrin, Gabriel (3-WON; London, ON)

*Omega*-*syntactic**congruences*. (English summary) J. ... The main contribution of this paper lies in finding a*congruence*on X” induced by an w-language L (the w-*syntactic**congruence*S,), which can also be used to characterize L. ...##
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Learning regular omega languages

2016
*
Theoretical Computer Science
*

The second is based on the

doi:10.1016/j.tcs.2016.07.031
fatcat:pqhjgq3cvnf7toewzmodnecnia
*syntactic*forc, introduced in [14]. The third is introduced herein. ... Three variations of the algorithm learn three different canonical representations of*omega*regular languages, using the notion of families of dfas. ... The*syntactic*fdfa corresponds to the notion of syntatic family of right*congruences*, introduced in [14] . The recurrent fdfa is introduced herein. ...##
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Learning Regular Omega Languages
[chapter]

2014
*
Lecture Notes in Computer Science
*

The second is based on the

doi:10.1007/978-3-319-11662-4_10
fatcat:bs5bugjxfrcobmua46l4ektxya
*syntactic*forc, introduced in [14]. The third is introduced herein. ... Three variations of the algorithm learn three different canonical representations of*omega*regular languages, using the notion of families of dfas. ... The*syntactic*fdfa corresponds to the notion of syntatic family of right*congruences*, introduced in [14] . The recurrent fdfa is introduced herein. ...##
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Regular omega-Languages with an Informative Right Congruence

2018
*
Electronic Proceedings in Theoretical Computer Science
*

The right

doi:10.4204/eptcs.277.19
fatcat:vw4areu5brau3nurhwnfzv4idi
*congruence*of a regular*omega*-language is not informative enough; many regular*omega*-languages have a trivial right*congruence*, and in general it is not always possible to define an*omega*-automaton ... The class of weak regular*omega*-languages does have an informative right*congruence*. ... of the relation between the*syntactic*right*congruence*of a language and its minimal acceptor in learning algorithms. ...##
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Efficient Algorithms for Morphisms over Omega-Regular Languages
[article]

2015
*
arXiv
*
pre-print

Morphisms to finite semigroups can be used for recognizing

arXiv:1509.06215v2
fatcat:tmddlly5jfeehkxlcxj4dydkni
*omega*-regular languages. ... We give a quadratic-time algorithm for computing the*syntactic*morphism from any given strongly recognizing morphism, thereby showing that minimization is easy as well. ... The relation ≡ is closely related to the*syntactic**congruence*, as confirmed by the following result: Proposition 10 The quotient semigroup S/≡ is isomorphic to A + /≡ L . Proof. ...##
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Semigroups and Automata on Infinite Words
[chapter]

1995
*
Semigroups, Formal Languages and Groups
*

Now the lower bound of the

doi:10.1007/978-94-011-0149-3_3
fatcat:baawnkgzrbdenmohs5wv3mgr6y
*congruences*that saturate P also saturates P and is called the*syntactic**congruence*of P . ... only if, for every x ∈ S 1 f , xu ∈ P ω ⇐⇒ xv ∈ P ω (11.1) The*syntactic*Wilke algebra of P is the quotient of S by the*syntactic**congruence*of P . ...##
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A Homomorphism Concept for omega-Regularity

1994
*
BRICS Report Series
*

<br /> <br />In this paper, we propose such a concept based on Families of Right

doi:10.7146/brics.v1i11.21659
fatcat:cusz7iai2vaoxkpr2sbyvtqcqm
*Congruences*(Maler and Staiger 93), which we view as a recognizing structures. ... The*syntactic**congruences*of Arnold 2] provide canonical algebraic structures for !-regular languages. ... But if minimization is involved, there need not be an exponential gain in using LFORCs instead of Arnold's*syntactic**congruences*, since during minimization LFORCs may blow up whereas Arnold's*congruences*...##
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Ehrenfeucht-Fraisse Games on Omega-Terms
[article]

2013
*
arXiv
*
pre-print

In this paper we introduce Ehrenfeucht-Fraisse games on

arXiv:1310.3195v1
fatcat:p65mszja5ndr7nqm3nvihl3vre
*omega*-terms. To this end we assign a labeled linear order to every*omega*-term. ... In order to show that a given fragment satisfies some identity of*omega*-terms, one can use Ehrenfeucht-Fraisse games on word instances of the*omega*-terms. ... The*syntactic**congruence*of L is the equivalence relation ≡ L on A * defined by u ≡ L v if xuy ∈ L is equivalent to xvy ∈ L for all x, y ∈ A * . In fact, ≡ L is a monoid*congruence*on A * . ...##
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"Decision Procedures: An Algorithmic Point of View," by Daniel Kroening and Ofer Strichman, Springer-Verlag, 2008

2013
*
Journal of automated reasoning
*

Section 4.1 presents one algorithm for

doi:10.1007/s10817-013-9295-4
fatcat:3wcuzym5krhc5eg33mansxlo2m
*congruence*closure based on [4] . ... However, the presentation is brief and, while a more thorough set of references on*congruence*closure can be found in the bibliography of chapter 4, it would have been nice to see more details on*congruence*...##
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First-Order logic and its Infinitary Quantifier Extensions over Countable Words
[article]

2021
*
arXiv
*
pre-print

The

arXiv:2107.01468v1
fatcat:k5zie3jeibgkrfapfgqzdoazhe
*omega*power of a word w is defined as w ω ::= i∈ω w. The*omega** power of a word w, denoted by w ω * , is the concatenation of*omega** many w's. ... The first (resp. second) disjunct guesses a cut towards which this*omega*(resp.*omega** ) sequence approaches. ...##
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A Novel Learning Algorithm for Büchi Automata based on Family of DFAs and Classification Trees
[article]

2017
*
arXiv
*
pre-print

We implement the first publicly available library ROLL (Regular

arXiv:1610.07380v2
fatcat:pd5g2gzyybbp5mkze5gvfq7wj4
*Omega*Language Learning ), which consists of all ω-regular learning algorithms available in the literature and the new algorithms proposed ... We use Σ * / ∽ to denote the equivalence classes of the right*congruence*∽. A finite right*congruence*is a right*congruence*with a finite index. ... We define the right*congruences*≈ u P , ≈ u S , and ≈ u R for progress automata A u of periodic,*syntactic*, and recurrent FDFA respectively as follows: x ≈ u P y iff ∀v ∈ Σ * , u(xv) ω ∈ L ⇐⇒ u(yv) ω ∈ ...##
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Quantifier Alternation in Two-Variable First-Order Logic with Successor Is Decidable
[article]

2012
*
arXiv
*
pre-print

We give a single identity of

arXiv:1212.6500v1
fatcat:h4nl5wfj7rddrhuvuiu4vubqpu
*omega*-terms for each level of this hierarchy. ... For every m ≥ 2 we give a single identity of*omega*-terms such that a language is definable in FO 2 m [<, suc] if and only if its*syntactic*semigroup satisfies this identity. ... The relation ≡ L over A + is a*congruence*and the semigroup A + /≡ L , also denoted by Synt(L) and called the*syntactic*semigroup of L, is the unique minimal semigroup recognizing L. ...##
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Page 1159 of Mathematical Reviews Vol. , Issue 98B
[page]

1998
*
Mathematical Reviews
*

Summary: “Several well-founded

*syntactic*orderings have been proposed in the literature for proving the termination of rewrite systems. ... Confluence results are obtained for lambda calculus with beta, eta and*omega*rules, lambda cal- culi with restricted expansion rules and for (first- and higher-order) term rewriting systems for which all ...##
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Operations on Weakly Recognizing Morphisms
[article]

2016
*
arXiv
*
pre-print

Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of

arXiv:1603.05376v2
fatcat:gfdsgl4mc5asvmwtummdqqjwiu
*omega*-regular languages, i.e., a set of infinite words is weakly recognizable by such ... The relation ≡ L was introduced by Arnold [1] ; it is called the*syntactic**congruence*of L. ... The*congruence*classes of ≡ L form the so-called*syntactic*semigroup A + /≡ L and the*syntactic*morphism h L : A + → A + /≡ L is the natural quotient map. If L ⊆ A * (resp. ...##
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On Completeness of Omega-Regular Algebras
[chapter]

2012
*
Lecture Notes in Computer Science
*

*Omega*-regular algebras axiomatise the equational theory of

*omega*-regular expressions as induced by

*omega*-regular language identity. ... Wagner presented an

*omega*-regular algebra which requires recursively defined side conditions in some of its axioms. ... Wilke [17] has proposed a two-sorted semigroup-based approach to ω-regular languages that adapts the

*syntactic*-monoid approach for regular languages [13] . ...

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