Irène Guessarian

Window subsequence problems for compressed texts

Given two strings (a text t of length n and a pattern p) and a natural number w, window subsequence problems consist in deciding whether p occurs as a subsequence of t and/or finding the number of size (at most) w windows of text t which contain pattern p as a subsequence, i.e. the letters of pattern p occur in the text window, in the same order as in p, but not necessarily consecutively (they may be interleaved with other letters). We are searching for subsequences in a text which is compressed using Lempel-Ziv-like compression algorithms, without decompressing the text, and we would like our algorithms to be almost optimal, in the sense that they run in time O(m) where m is the size of the compressed text. The pattern is uncompressed (because the compression algorithms are evolutive: various occurrences of a same pattern look different in the text).

Transforming constraint logic programs

Abstract We study “a la Tamaki-Sato” transformations of constraint logic programs. We give an operational and fixpoint semantics of our constraint logic programs; we extend the Tamaki-Sato transformation system into a transformation system for constraint programs including fold-unfold, substitution, thinning and fattening, and constraint simplifications; we give a direct proof of its correctness which is simpler than the Tamaki-Sato proof.

Deciding Boundedness for Uniformly Connected Datalog Programs

We prove that boundedness is decidable for uniformly (and more generally strongly) connected Datalog programs. As for chain programs, which are a special case of uniformly connected programs, the proof is done by reducing the boundedness problem to context-free language finiteness. The same reduction technique could be used for containment problems.

On Continuous Completions

This paper is devoted to the study of various completions of posets which preserve the algebraic or ordering structure of the given poset.

Program transformations and algebraic semantics

Abstract We study transformations and equivalences of recursive program schemes. We give an optimization algorithm which recognizes and removes all parts of a program scheme which do not affect its final output. This result leads to a syntactic way of suppressing some erroneous loops in programs and can be used to prove that equivalence of recursive program schemes is solvable under particular conditions.

Window-accumulated subsequence matching problem is linear

Abstract Given two strings, text t of length n , and pattern p = p 1 …p k of length k , and given a natural number w , the subsequence matching problem consists in finding the number of size w windows of text t which contain pattern p as a subsequence, i.e. the letters p 1 ,…,p k occur in the window, in the same order as in p , but not necessarily consecutively (they may be interleaved with other letters). Subsequence matching is used for finding frequent patterns and association rules in databases. We generalize the Knuth–Morris–Pratt (KMP) pattern matching algorithm; we define a non-conventional kind of RAM, the MP-RAMs which model more closely the microprocessor operations; we design an O (n) on-line algorithm for solving the subsequence matching problem on MP-RAMs.

Some Fixpoint Techniques in Algebraic Structures and Applications to Computer Science

Publisher Summary Finding the final state that corresponds to a stable state—that is, a fixpoint of the set of recursive equations—and finding this stable state in the most effective and efficient way—that is, computing the fixpoint as fast as possible and/or using as little space as possible—form the core of the fixpoint theory. This chapter presents the connections and common points between the various fixpoint methods that are used. Nearly all the fixpoint techniques, which are usable, rely on an induction principle: They all compute the fixpoint by induction, using successive substitutions. However, this simple method leads to efficient results. In some cases, it is shown that fixpoint techniques can even be used to transform cheaply a system whose solution, or stable state, is hard to find into an equivalent system that can be easily solved. In other cases, for example, a wide class of recursive queries in deductive data bases, fixpoint techniques allow one to solve the queries efficiently, without computing irrelevant or duplicate facts.

An Automaton Characterization of Fairness in SCCS

We describe various kinds of fairness (mainly weak and strong fairness) for finite state SCCS processes by providing an automaton-theoretic characterization of the classes of fair languages. To this end, we introduce a variant of Muller automata, the T-automata, which still recognize the class of ω-regular languages, and which characterize the classes of fair languages.

Survey on classes of interpretations and some of their applications

We introduce classes of interpretations. We characterize the free and Herbrand interpretations for a class. We define the algebraic, equational, relational and first-order classes of interpretations, study their properties and relate them to the literature. We apply this study to derive complete proof systems for deducing (in some (in) equational logic) all (in) equalitions valid in a class.

Newton representation of functions over natural integers having integral difference ratios

Different questions lead to the same class of functions from natural integers to integers: those which have integral difference ratios, i.e. verifying f(a) - f(b) ≡ 0 (mod (a - b)) for all a > b. We characterize this class of functions via their representations as Newton series. This class, which obviously contains all polynomials with integral coefficients, also contains unexpected functions, for instance, all functions x ↦ ⌊e1/a ax x!⌋, with a ∈ ℤ\{0, 1}, and a function equal to ⌊e x!⌋ except on 0. Finally, to study the complement class, we look at functions ℕ → ℝ which are not uniformly close to any function having integral difference ratios.