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MyhillNerode relations on automatic systems and the completeness of Kleene algebra
 In STACS 2001 (Dresden), volume 2010 of Lecture
"... Abstract. It is well known that finite square matrices over a Kleene algebra again form a Kleene algebra. This is also true for infinite matrices under suitable restrictions. One can use this fact to solve certain infinite systems of inequalities over a Kleene algebra. Automatic systems are a specia ..."
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special class of infinite systems that can be viewed as infinitestate automata. Automatic systems can be collapsed using Myhill–Nerode relations in much the same way that finite automata can. The Brzozowski derivative on an algebra of polynomials over a Kleene algebra gives rise to a triangular automatic
On the MyhillNerode Theorem for Trees
"... The MyhillNerode Theorem as stated in [6] says that for a set R of strings over a finite alphabet, the following statements are equivalent: (i) R is regular (ii) R is a union of classes of a rightinvariant equivalence relation of index finite (iii) the relation R is of finite index, where x R y i ..."
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The MyhillNerode Theorem as stated in [6] says that for a set R of strings over a finite alphabet, the following statements are equivalent: (i) R is regular (ii) R is a union of classes of a rightinvariant equivalence relation of index finite (iii) the relation R is of finite index, where x R y i
MyhillNerode methods for hypergraphs
 IN PROC. OF ISAAC 2013, LNCS
, 2013
"... We introduce a method of applying MyhillNerode methods from formal language theory to hypergraphs and show how this method can be used to obtain the following parameterized complexity results. – Hypergraph Cutwidth (deciding whether a hypergraph on n vertices has cutwidth at most k) is lineartime ..."
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We introduce a method of applying MyhillNerode methods from formal language theory to hypergraphs and show how this method can be used to obtain the following parameterized complexity results. – Hypergraph Cutwidth (deciding whether a hypergraph on n vertices has cutwidth at most k) is linear
MYHILLNERODE Congruence — Definition
"... A sequential transducer [3, 4] is a weighted automaton ¡£ ¢ ¡¥ ¤ ¡§¦¨¡� © ¡� � � such that for at most � one �, ..."
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A sequential transducer [3, 4] is a weighted automaton ¡£ ¢ ¡¥ ¤ ¡§¦¨¡� © ¡� � � such that for at most � one �,
MyhillNerode theorem for recognizable tree series revisited
, 2007
"... In this contribution the MyhillNerode congruence relation on tree series is reviewed and a more detailed analysis of its properties is presented. It is shown that, if a tree series is deterministically recognizable over a zerodivisor free and commutative semiring, then the MyhillNerode congruence ..."
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In this contribution the MyhillNerode congruence relation on tree series is reviewed and a more detailed analysis of its properties is presented. It is shown that, if a tree series is deterministically recognizable over a zerodivisor free and commutative semiring, then the MyhillNerode
The MyhillNerode Theorem based on Regular Expressions
 The Archive of Formal Proofs. http://afp.sourceforge.net/develentries/ MyhillNerode.shtml
, 2011
"... Abstract. There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOLbased theorem provers. The reason is th ..."
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Cited by 13 (2 self)
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reasoning infrastructure comes for free. We show in this paper that a central result from formal language theory—the MyhillNerode theorem—can be recreated using only regular expressions. 1
The MyhillNerode Theorem for Recognizable Tree Series
"... Abstract. In this paper we prove a MyhillNerode theorem for recognizable tree series over commutative semifields and thereby present a minimization of bottomup finite state weighted tree automata over a commutative semifield, where minimal means with respect to the number of states among all equiv ..."
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Abstract. In this paper we prove a MyhillNerode theorem for recognizable tree series over commutative semifields and thereby present a minimization of bottomup finite state weighted tree automata over a commutative semifield, where minimal means with respect to the number of states among all
MyhillNerode Theorem for Sequential Transducers over Unique GCDMonoids
"... Abstract. We generalize the classical MyhillNerode theorem for finite automata to the setting of sequential transducers over unique GCDmonoids, which are cancellative monoids in which every two nonzero elements admit a unique greatest common (left) divisor. We prove that a given formal power serie ..."
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series is sequential, if and only if it is directed and our MyhillNerode equivalence relation has finite index. As in the classical case, our MyhillNerode equivalence relation also admits the construction of a minimal (with respect to the number of states) sequential transducer recognizing the given
Results 1  10
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3,625