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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.  ... 

Learning regular omega languages

Dana Angluin, Dana Fisman
2016 Theoretical Computer Science  
The second is based on the 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.  ... 
doi:10.1016/j.tcs.2016.07.031 fatcat:pqhjgq3cvnf7toewzmodnecnia

Learning Regular Omega Languages [chapter]

Dana Angluin, Dana Fisman
2014 Lecture Notes in Computer Science  
The second is based on the 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.  ... 
doi:10.1007/978-3-319-11662-4_10 fatcat:bs5bugjxfrcobmua46l4ektxya

Regular omega-Languages with an Informative Right Congruence

Dana Angluin, Dana Fisman
2018 Electronic Proceedings in Theoretical Computer Science  
The right 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.  ... 
doi:10.4204/eptcs.277.19 fatcat:vw4areu5brau3nurhwnfzv4idi

Efficient Algorithms for Morphisms over Omega-Regular Languages [article]

Lukas Fleischer, Manfred Kufleitner
2015 arXiv   pre-print
Morphisms to finite semigroups can be used for recognizing 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.  ... 
arXiv:1509.06215v2 fatcat:tmddlly5jfeehkxlcxj4dydkni

Semigroups and Automata on Infinite Words [chapter]

Dominique Perrin, Jean-Eric Pin
1995 Semigroups, Formal Languages and Groups  
Now the lower bound of the 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 .  ... 
doi:10.1007/978-94-011-0149-3_3 fatcat:baawnkgzrbdenmohs5wv3mgr6y

A Homomorphism Concept for omega-Regularity

Nils Klarlund
1994 BRICS Report Series  
<br /> <br />In this paper, we propose such a concept based on Families of Right 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  ... 
doi:10.7146/brics.v1i11.21659 fatcat:cusz7iai2vaoxkpr2sbyvtqcqm

Ehrenfeucht-Fraisse Games on Omega-Terms [article]

Martin Huschenbett, Manfred Kufleitner
2013 arXiv   pre-print
In this paper we introduce Ehrenfeucht-Fraisse games on 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 * .  ... 
arXiv:1310.3195v1 fatcat:p65mszja5ndr7nqm3nvihl3vre

"Decision Procedures: An Algorithmic Point of View," by Daniel Kroening and Ofer Strichman, Springer-Verlag, 2008

Clark Barrett
2013 Journal of automated reasoning  
Section 4.1 presents one algorithm for 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  ... 
doi:10.1007/s10817-013-9295-4 fatcat:3wcuzym5krhc5eg33mansxlo2m

First-Order logic and its Infinitary Quantifier Extensions over Countable Words [article]

Bharat Adsul, Saptarshi Sarkar, A.V. Sreejith
2021 arXiv   pre-print
The 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.  ... 
arXiv:2107.01468v1 fatcat:k5zie3jeibgkrfapfgqzdoazhe

A Novel Learning Algorithm for Büchi Automata based on Family of DFAs and Classification Trees [article]

Yong Li, Yu-Fang Chen, Lijun Zhang, Depeng Liu
2017 arXiv   pre-print
We implement the first publicly available library ROLL (Regular 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 ∈  ... 
arXiv:1610.07380v2 fatcat:pd5g2gzyybbp5mkze5gvfq7wj4

Quantifier Alternation in Two-Variable First-Order Logic with Successor Is Decidable [article]

Manfred Kufleitner, Alexander Lauser
2012 arXiv   pre-print
We give a single identity of 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.  ... 
arXiv:1212.6500v1 fatcat:h4nl5wfj7rddrhuvuiu4vubqpu

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  ... 

Operations on Weakly Recognizing Morphisms [article]

Lukas Fleischer, Manfred Kufleitner
2016 arXiv   pre-print
Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of 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.  ... 
arXiv:1603.05376v2 fatcat:gfdsgl4mc5asvmwtummdqqjwiu

On Completeness of Omega-Regular Algebras [chapter]

Michael R. Laurence, Georg Struth
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] .  ... 
doi:10.1007/978-3-642-33314-9_12 fatcat:wnhk74ykdja2xhczjhiylzqsva
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