Nicolae Santean

On the robustness of primitive words

We investigate the effect on primitive words of point mutations (inserting or deleting symbols, substituting a symbol for another one), of morphisms, and of the operation of taking prefixes. Several ways of producing primitive words are obtained in this framework.

Detecting palindromes, patterns and borders in regular languages

Given a language L and a non-deterministic finite automaton M, we consider whether we can determine efficiently (in the size of M) if M accepts at least one word in L, or infinitely many words. Given that M accepts at least one word in L, we consider how long a shortest word can be. The languages L that we examine include the palindromes, the non-palindromes, the k-powers, the non-k-powers, the powers, the non-powers (also called primitive words), the words matching a general pattern, the bordered words, and the unbordered words.

On the intersection of regex languages with regular languages

In this paper we revisit the semantics of extended regular expressions (regex), defined succinctly in the 90s [A.V. Aho, Algorithms for finding patterns in strings, in: Jan van Leeuwen (Ed.), Handbook of Theoretical Computer Science, in: Algorithms and Complexity, vol. A, Elsevier and MIT Press, 1990, pp. 255-300] and rigorously in 2003 by Campeanu, Salomaa and Yu [C. Campeanu, K. Salomaa, S. Yu, A formal study of practical regular expressions, IJFCS 14 (6) (2003) 1007-1018], when the authors reported an open problem, namely whether regex languages are closed under the intersection with regular languages. We give a positive answer; and for doing so, we propose a new class of machines - regex automata systems (RAS) - which are equivalent to regex. Among others, these machines provide a consistent and convenient method of implementing regex in practice. We also prove, as a consequence of this closure property, that several languages, such as the mirror language, the language of palindromes, and the language of balanced words are not regex languages.

Representation and uniformization of algebraic transductions

This paper explores different means of representation for algebraic transductions, i.e., word relations realized by pushdown transducers. The relevance of this work lies more in its point of view rather than any particular result. We are aiming at giving specific techniques for obtaining, or perhaps explaining, decompositions of algebraic (and incidentally, rational) relations, relying solely on their “machine” definition rather than some complex algebraic apparatus. From this point of view, we are hoping to have demystified the heavy formalism employed in the present literature. Some of the novelties of our work are: the use of “stack languages” and “embeddings,” which eliminate the need of arbitrary context-free languages in our characterizations, the study of uniformizations for algebraic transductions and the use of the so-called stack transductions for exposing the anatomy of pushdown transducers.

ON THE EXISTENCE OF LOOKAHEAD DELEGATORS FOR NFA

We investigate deterministically simulating (i.e., solving the membership problem for) nondeterministic finite automata (NFA), relying solely on the NFAs resources (states and transitions). Unlike the standard NFA simulation, involving an algorithm which stores at each step all the states reached nondeterministically while reading the input, we consider deterministic finite automata (DFA) with lookahead, which choose the “right” NFA transitions based on a fixed number of input symbols read ahead. This concept, known as lookahead delegation, arose in a formal study of web services composition and its subsequent practical applications. Here we answer several related questions, such as “when is lookahead delegation possible?” and “how hard is it to find a delegator with a given lookahead buffer size?”. In particular, we show that only finite languages have the property that all their NFA have delegators. This implies, among others, that delegation is a machine property, rather than a language property. We also prove that the existence of lookahead delegators for unambiguous NFA is decidable, thus partially solving an open problem. Finally, we show that finding delegators (even for a given buffer size) is hard in general, and is more efficient for unambiguous NFA, and we give an algorithm and a compact characterization for NFA delegation in general.

On implementing recognizable transductions

Recognizable transductions constitute a proper subclass of rational transductions, characterized by the well-known Mezeis Theorem. We propose a family of transducers which reflect accurately this characterization, and we study their properties and their algorithmic aspects. We base our construct on the observation that there is a connection between recognizable transductions and languages consisting of edit strings. More specifically, we define a saturated transducer to be a transducer with the property that accepts all possible edit strings corresponding to each accepted pair of words, when viewed as an automaton over the edit alphabet. We revisit the theory behind recognizable transductions from the point of view of saturated transducers, and we give constructive proofs as well as descriptional complexities for their closure properties. In particular, we give a novel and rather non-trivial algorithm for constructing a saturated transducer for the concatenation of two saturated transductions. Finally, we discuss the natural role of these objects in edit distance problems. Perhaps the relevance of this work lies more in its point of view and initiative rather than in any particular result.

Finite Automata, Palindromes, Powers, and Patterns

Given a language Land a nondeterministic finite automaton M, we consider whether we can determine efficiently (in the size of M) if Maccepts at least one word in L, or infinitely many words. Given that Maccepts at least one word in L, we consider how long the shortest word can be. The languages Lthat we examine include the palindromes, the non-palindromes, the k-powers, the non-k-powers, the powers, the non-powers (also called primitive words), and words matching a general pattern.

On the definition of stochastic λ-transducers

We propose a formal definition for the general notion of stochastic transducer, called stochastic λ-transducer. Our definition is designed with two objectives in mind: (i) to extend naturally the established notion of stochastic automaton with output—as defined in the classic books of [A. Paz, Introduction to Probabilistic Automata, Academic Press, New York and London, 1971; P. Starke, Abstract Automata, North-Holland, Academic Press, 1972.]—by permitting pairs of input-output words of different lengths; (ii) to be compatible with the more general notion of weighted transducer so that one can apply tools of weighted transducers to address certain computational problems involving stochastic transducers. The new transducers can be used to model stochastic input-output processes that cannot be modelled using classical stochastic automata with output.

On weakly ambiguous finite transducers

By weakly ambiguous (finite) transducers we mean those transducers that, although being ambiguous, may be viewed to be at arms length from unambiguity. We define input-unambiguous (IU) and input-deterministic (ID) transducers, and transducers with finite codomain (FC). IU transductions are characterized by nondeterministic bimachines and ID transductions can be represented as a composition of sequential functions and finite substitutions. FC transductions are recognizable and can be expressed as finite unions of subsequential functions. We place these families along with uniformly ambiguous (UA) and finitely ambiguous (FA) transductions in a hierarchy of ambiguity. Finally, we show that restricted nondeterministic bimachines characterize FA transductions. Perhaps the most important aspect of this work consists in defining nondeterministic bimachines and describing their power by linking them with weakly ambiguous finite transducers (IU and FA).

On the closure of pattern expressions languages under intersection with regular languages

In this paper we address a standing question on pattern expressions (PE), namely whether the family of PE languages is closed under the intersection with regular languages. Since this family is not closed under complement, but is closed under reversal, another natural question has frequently been raised in the recent years, on whether particular languages such as the mirror language and the language of palindromes are PE languages. We give answers to these and other related questions as well, thus providing an insight on their descriptional power.