Hellis Tamm

Quotient complexities of atoms of regular languages

An atom of a regular language L with n (left) quotients is a non-empty intersection of uncomplemented or complemented quotients of L, where each of the n quotients appears in a term of the intersection. The quotient complexity of L, which is the same as the state complexity of L, is the number of quotients of L. We prove that, for any language L with quotient complexity n, the quotient complexity of any atom of L with r complemented quotients has an upper bound of 2n−1 if r=0 or r=n, and

COMPLEXITY OF ATOMS OF REGULAR LANGUAGES

1+\sum_{k=1}^{r} \sum_{h=k+1}^{k+n-r} C_{h}^{n} \cdot C_{k}^{h}

Implementing a Declarative String Query Language with String Restructuring

otherwise, where

Design and implementation of a string database query language

C_j^i

Minimal DFA for symmetric difference NFA

is the binomial coefficient. For each

Bideterministic automata and minimal representations of regular languages

n\geqslant 1

New Interpretation and Generalization of the Kameda-Weiner Method

, we exhibit a language whose atoms meet these bounds.

Adding string processing capabilities to data management systems

Electronic version of an article published as International Journal of Foundations of Computer Science, 24(07), 2013, 1009–1027. http://dx.doi.org/10.1142/S0129054113400285

Generalization of the Double-Reversal Method of Finding a Canonical Residual Finite State Automaton

We describe the design and implementation of a declarative database query language for manipulating character strings. The language can be used to create logical predicates expressing structural properties of strings and relations between several strings. The predicates can be used to query strings in databases, and by leaving variables uninstantiated, also to generate new strings not contained in the database. A full working system was implemented as an extension of an object-oriented database management system and its query language. The declarative expressions are evaluated by first performing a compilation transforming them to nondeterministic finite state automata and then by simulating these automata using a depth-first search engine. The system checks the safety of each string-manipulation query in advance to preclude infinite ones. This safety checking provides also a compile-time loop-checking mechanism for the search engine, improving its eficiency.

ON TRANSITION MINIMALITY OF BIDETERMINISTIC AUTOMATA

Current data management and information retrieval systems lack advanced string processing capabilities needed in string-oriented application areas like computational molecular biology. Several theoretical models for string processing have been proposed but they either have not been implemented in practice or the implementations are too restricted or platform-dependent to be generally useful. In this article, we introduce the language Alignment Declarations designed for string querying and restructuring. The language extends the capabilities of existing database query languages by allowing the user to define database predicates that express structural properties of strings (e.g. containment of certain patterns) or relations between several strings (e.g. similarity measures). These predicates can be created and executed within the same database session and also stored for later sessions. We also describe the design and implementation of a working system.