Linear automaton transformations
Anil Nerode
- Vol. 9, Iss: 4, pp 541-544
Reads0
Chats0
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 satisfyingread more
Citations
More filters
Journal ArticleDOI
A Minimized Assumption Generation Method for Component-Based Software Verification
TL;DR: The key idea of this method is finding the minimal assumptions in the search spaces of the candidate assumptions of the assume-guarantee verification of component-based software.
Book ChapterDOI
Syntactic complexity of Prefix-, Suffix-, and Bifix-free regular languages
TL;DR: It is proved that nn-2 is a tight upper bound for prefix-free regular languages, and properties of the syntactic semigroups of suffix- and bifix- free regular languages are presented, and tight upper bounds on their size are conjecture.
Posted Content
Going Higher in First-Order Quantifier Alternation Hierarchies on Words
Thomas Place,Marc Zeitoun +1 more
TL;DR: In this paper, the authors investigated quantifier alternation hierarchies in first-order logic on finite words, and proved that one can decide membership of a regular language in the levels $\mathcal{B}{\Sigma}_2$ (finite boolean combinations of formulas having only one alternation) and ${B}_3$ (formulas having only two alternations and beginning with an existential block).
Contributions to the theory and applications of tree languages
TL;DR: This thesis is concerned with theoretical as well as practical aspects of tree languages and consists of an introduction and eight papers, organised into three parts.
Journal ArticleDOI
Canonicity in GFG and Transition-Based Automata
Bader Abu Radi,Orna Kupferman +1 more
TL;DR: Limiting attention to the safe components is useful, and implies that the only minimal tDCWs that have no canonical form are these for which the transition to the GFG model results in strictly smaller automaton, which do have a canonical minimal form.
References
More filters
Book ChapterDOI
Representation of Events in Nerve Nets and Finite Automata
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.