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
Proceedings ArticleDOI
Matching implementations to specifications: the corner cases of ioco
R. Janssen,Jan Tretmans +1 more
TL;DR: This paper shows that given a specification, one can construct in a standard way a canonical conforming implementation that is very 'close' to the specification; and a refinement preorder on specification models can be defined such that a refined model allows less ioco-conforming implementations.
Book ChapterDOI
Minimal unambiguous εNFA
TL;DR: An algorithm for compactifying eNFA is presented that exploits the union principle and has the following property: if the algorithm returns an unambiguous automaton, then this automaton is the transition minimal eN FA.
Posted Content
Knowledge extraction from the learning of sequences in a long short term memory (LSTM) architecture
Ikram Chraibi Kaadoud,Ikram Chraibi Kaadoud,Nicolas P. Rougier,Nicolas P. Rougier,Frédéric Alexandre +4 more
TL;DR: A general method to extract knowledge from a recurrent neural network that has learnt to detect if a given input sequence is valid or not, according to an unknown generative automaton is introduced.
Book ChapterDOI
Advanced Process Discovery Techniques
TL;DR: This chapter focuses on more advanced process discovery techniques, and insights into the strengths and weaknesses of the various approaches support the correct interpretation and effective use of the discovered models.
Proceedings ArticleDOI
Assume-Guarantee Tools for Component-Based Software Verification
TL;DR: A minimized assumption generation method and its associated tools for L*-based assume-guarantee verification of component-based software by model checking and experience so far indicates that the implemented tools are potential for verifying practical component- based software.
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.