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A Hierarchy of Automatic ω-Words having a Decidable MSO Theory

Vince Bárány (2008)

RAIRO - Theoretical Informatics and Applications

We investigate automatic presentations of ω-words. Starting points of our study are the works of Rigo and Maes, Caucal, and Carton and Thomas concerning lexicographic presentation, MSO-interpretability in algebraic trees, and the decidability of the MSO theory of morphic words. Refining their techniques we observe that the lexicographic presentation of a (morphic) word is in a certain sense canonical. We then generalize our techniques to a hierarchy of classes of ω-words enjoying the above...

Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm

Grzegorz Bancerek (2014)

Formalized Mathematics

Educational content for abstract reduction systems concerning reduction, convertibility, normal forms, divergence and convergence, Church- Rosser property, term rewriting systems, and the idea of the Knuth-Bendix Completion Algorithm. The theory is based on [1].

Adhesive and quasiadhesive categories

Stephen Lack, Paweł Sobociński (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.

Adhesive and quasiadhesive categories

Stephen Lack, Paweł Sobociński (2010)

RAIRO - Theoretical Informatics and Applications

We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.

Algebra grammars

Radim Bělohlávek (1995)

Acta Mathematica et Informatica Universitatis Ostraviensis

Arbology: Trees and pushdown automata

Bořivoj Melichar, Jan Janoušek, Tomas Flouri (2012)

Kybernetika

We present a unified and systematic approach to basic principles of Arbology, a new algorithmic discipline focusing on algorithms on trees. Stringology, a highly developed algorithmic discipline in the area of string processing, can use finite automata as its basic model of computation. For various kinds of linear notations of ranked and unranked ordered trees it holds that subtrees of a tree in a linear notation are substrings of the tree in the linear notation. Arbology uses pushdown automata...

Bidirectional string assembling systems

Martin Kutrib, Matthias Wendlandt (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We introduce and investigate several variants of a bidirectional string assembling system, which is a computational model that generates strings from copies of assembly units. The underlying mechanism is based on two-sided piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. The generative capacities and the relative power of the variants are our main interest. In particular, we prove that bidirectional string assembling system generate languages...

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