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Polyabelian loops and Boolean completeness

François Lemieux, Cristopher Moore, Denis Thérien (2000)

Commentationes Mathematicae Universitatis Carolinae

We consider the question of which loops are capable of expressing arbitrary Boolean functions through expressions of constants and variables. We call this property Boolean completeness. It is a generalization of functional completeness, and is intimately connected to the computational complexity of various questions about expressions, circuits, and equations defined over the loop. We say that a loop is polyabelian if it is an iterated affine quasidirect product of Abelian groups; polyabelianness...

Polynomial languages with finite antidictionaries

Arseny M. Shur (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We tackle the problem of studying which kind of functions can occur as complexity functions of formal languages of a certain type. We prove that an important narrow subclass of rational languages contains languages of polynomial complexity of any integer degree over any non-trivial alphabet.

Polynomial languages with finite antidictionaries

Arseny M. Shur (2008)

RAIRO - Theoretical Informatics and Applications

We tackle the problem of studying which kind of functions can occur as complexity functions of formal languages of a certain type. We prove that an important narrow subclass of rational languages contains languages of polynomial complexity of any integer degree over any non-trivial alphabet.

Polynomial time algorithms for two classes of subgraph problem

Sriraman Sridharan (2008)

RAIRO - Operations Research

We design a O(n3) polynomial time algorithm for finding a (k-1)- regular subgraph in a k-regular graph without any induced star K1,3(claw-free). A polynomial time algorithm for finding a cubic subgraph in a 4-regular locally connected graph is also given. A family of k-regular graphs with an induced star K1,3 (k even, k ≥ 6), not containing any (k-1)-regular subgraph is also constructed.

Polynomial time bounded truth-table reducibilities to padded sets

Vladimír Glasnák (2000)

Commentationes Mathematicae Universitatis Carolinae

We study bounded truth-table reducibilities to sets of small information content called padded (a set is in the class f -PAD of all f -padded sets, if it is a subset of { x 10 f ( | x | ) - | x | - 1 ; x { 0 , 1 } * } ). This is a continuation of the research of reducibilities to sparse and tally sets that were studied in many previous papers (for a good survey see [HOW1]). We show necessary and sufficient conditions to collapse and separate classes of bounded truth-table reducibilities to padded sets. We prove that depending on two properties of a...

Polynomially Bounded Sequences and Polynomial Sequences

Hiroyuki Okazaki, Yuichi Futa (2015)

Formalized Mathematics

In this article, we formalize polynomially bounded sequences that plays an important role in computational complexity theory. Class P is a fundamental computational complexity class that contains all polynomial-time decision problems [11], [12]. It takes polynomially bounded amount of computation time to solve polynomial-time decision problems by the deterministic Turing machine. Moreover we formalize polynomial sequences [5].

Polynomials over the reals in proofs of termination : from theory to practice

Salvador Lucas (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

This paper provides a framework to address termination problems in term rewriting by using orderings induced by algebras over the reals. The generation of such orderings is parameterized by concrete monotonicity requirements which are connected with different classes of termination problems: termination of rewriting, termination of rewriting by using dependency pairs, termination of innermost rewriting, top-termination of infinitary rewriting, termination of context-sensitive rewriting, etc. We...

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