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Open AccessJournal ArticleDOI

Linear automaton transformations

Anil Nerode
- Vol. 9, Iss: 4, pp 541-544
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TLDR
For a finite commutative ring with unit the authors determine which linear transformations M: RN—+RN can be realized by finite automata.
Abstract
Let R be a nonempty set, let N consist of all non-negative rational integers, and denote by RN the set of all functions on N to R. If R is a ring, a map M: R"—>P^ is linear if M(rxfx+r2f2)=rx(Mfx) +r2(Mf2) for rx, r2 in R, fx, f2 in RN. For a finite commutative ring with unit we determine which linear transformations M: RN—+RN can be realized by finite automata. More precisely, let A, B he finite nonempty sets. A map M: AN—>BN is an automaton transformation if there exists a finite set Q, maps Mq: A X£>—><2, Mb: A XQ-*B, elements h in B, q in Q such that corresponding to each/ in AN there exists an h in QN satisfying

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Citations
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Journal ArticleDOI

Regular Expression Learning from Positive Examples Based on Integer Programming

TL;DR: This paper proposes multiscaling sample augmentation to capture the cycle patterns from single examples during the candidate’s construction phase, and uses common substrings to build regular expressions that capture patterns across multiple examples, and shows this algorithm is more general than those based on common prefixes or suffixes.
Journal ArticleDOI

Congruence-based proofs of the recognizability theorems for free many-sorted algebras

TL;DR: Several recognizability theorems for free single-sorted algebras are generalized to the field of many-sorts algebraes and purely algebraic proofs of them based on the concept of congruence are provided.
Book ChapterDOI

Methods via Automata and Bounded Treewidth

TL;DR: In the next few sections, a self-contained account of the aspects of classical formal language theory which the authors need will be given, starting with finite automata.
References
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Book ChapterDOI

Representation of Events in Nerve Nets and Finite Automata

S. C. Kleene
TL;DR: This memorandum is devoted to an elementary exposition of the problems and of results obtained on the McCulloch-Pitts nerve net during investigations in August 1951.