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Closure under union and composition of iterated rational transductions

D. Simplot, A. Terlutte (2010)

RAIRO - Theoretical Informatics and Applications

We proceed our work on iterated transductions by studying the closure under union and composition of some classes of iterated functions. We analyze this closure for the classes of length-preserving rational functions, length-preserving subsequential functions and length-preserving sequential functions with terminal states. All the classes we obtain are equal. We also study the connection with deterministic context-sensitive languages.

Clustering of vaguely defined objects

Libor Žák (2003)

Archivum Mathematicum

This paper is concerned with the clustering of objects whose properties cannot be described by exact data. These can only be described by fuzzy sets or by linguistic values of previously defined linguistic variables. To cluster these objects we use a generalization of classic clustering methods in which instead of similarity (dissimilarity) of objects, used fuzzy similarity (fuzzy dissimilarity) to define the clustering of fuzzy objects.

Co je LOGO?

Petr Štěpánek (1981)

Pokroky matematiky, fyziky a astronomie

Coalgebras for binary methods : properties of bisimulations and invariants

Hendrik Tews (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Coalgebras for endofunctors 𝒞 → 𝒞 can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors 𝒞 o p × 𝒞 → 𝒞 . This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many standard...

Coalgebras for Binary Methods: Properties of Bisimulations and Invariants

Hendrik Tews (2010)

RAIRO - Theoretical Informatics and Applications

Coalgebras for endofunctors 𝒞 → 𝒞 can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors 𝒞 o p × 𝒞 → 𝒞 . This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many...

Cobham's theorem for substitutions

Fabien Durand (2011)

Journal of the European Mathematical Society

The seminal theorem of Cobham has given rise during the last 40 years to a lot of work about non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let α and β be two multiplicatively independent Perron numbers. Then a sequence x ∈ A ℕ , where A is a finite alphabet, is both α -substitutive and β -substitutive if and only if x is ultimately periodic....

Cocktail: a tool for deriving correct programs.

Michael Franssen, Harrie De Swart (2004)

RACSAM

Cocktail is a tool for deriving correct programs from their specifications. The present version is powerful enough for educational purposes. The tool yields support for many sorted first order predicate logic, formulated in a pure type system with parametric constants (CPTS), as the specification language, a simple While-language, a Hoare logic represented in the same CPTS for deriving programs from their specifications and a simple tableau based automated theorem prover for verifying proof obligations....

Codes et motifs

Bodonirina Ratoandromanana (1989)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Codes that attain minimum distance in every possible direction

Gyula Katona, Attila Sali, Klaus-Dieter Schewe (2008)

Open Mathematics

The following problem motivated by investigation of databases is studied. Let 𝒞 be a q-ary code of length n with the properties that 𝒞 has minimum distance at least n − k + 1, and for any set of k − 1 coordinates there exist two codewords that agree exactly there. Let f(q, k)be the maximum n for which such a code exists. f(q, k)is bounded by linear functions of k and q, and the exact values for special k and qare determined.

Cohesiveness in promise problems

Ulrike Brandt, Hermann K.-G. Walter (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Promise problems have been introduced in 1985 by S. Even e.a. as a generalization of decision problems. Using a very general approach we study solvability and unsolvability conditions for promise problems of set and language families. We show, that cores of unsolvability are completely determined by partitions of cohesive sets. We prove the existence of cores in unsolvable promise problems assuming certain closure properties for the given set family. Connections to immune sets and complexity cores...

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