Catálogo de publicaciones - libros

The paper extends the notion of context-free LL() grammars to CD grammar systems using two different derivation modes, examines some of the properties of the resulting language families, and studies the possibility of parsing these languages deterministically, without backtracking.

We investigate the problems of testing membership in the subset of the positive numbers produced at the output of combinational circuits. These problems are a natural modification of those studied by McKenzie and Wagner (2003), where circuits computed sets of natural numbers. It turns out that the missing 0 has strong implications, not only because 0 can be used to test for emptiness. We show that the membership problem for the general case and for is PSPACE-complete, whereas it is NEXPTIME-hard if one allows 0. Furthermore, testing membership for is NL-complete (as opposed to -hard), and several other cases are resolved.

In the context of comparative analysis of protein-protein interaction graphs, we use a graph-based formalism to detect the preservation of a given protein complex (pattern graph) in the protein-protein interaction graph (target graph) of another species with respect to (w.r.t.) orthologous proteins. We give an efficient exponential-time randomized algorithm in case the occurrence of the pattern graph in the target graph is required to be exact. For approximate occurrences, we prove a tight inapproximability results and give four approximation algorithms that deal with bounded degree graphs, small ortholog numbers, linear forests and very simple yet hard instances, respectively.

The string pointer reduction system (SPRS) and the graph pointer reduction system (GPRS) are important formal models of gene assembly in ciliates. The reduction graph is a useful tool for the analysis of the SPRS, providing valuable information about the way that gene assembly is performed for a given gene. The GPRS is more abstract than the SPRS – not all information present in the SPRS is retained in the GPRS. As a consequence the reduction graph cannot be defined for the GPRS in general, but we show that it can be defined if we restrict ourselves to the so-called realistic overlap graphs (which correspond to genes occurring in nature). Defining the reduction graph within the GPRS allows one to carry over from the SPRS to the GPRS several results that rely on the reduction graph.

The simple intramolecular model for gene assembly in ciliates is particularly interesting because it can predict the correct assembly of all available experimental data, although it is not universal. The simple model also has a confluence property that is not shared by the general model. A previous formalization of the simple model through sorting of signed permutations is unsatisfactory because it effectively ignores one operation of the model and thus, it cannot be used to answer questions about parallelism in the model, or about measures of complexity. We propose in this paper a string-based model in which a gene is represented through its sequence of pointers and markers and its assembly is represented as a string rewriting process. We prove that this string-based model is equivalent to the permutation-based model as far as gene assembly is concerned, while it tracks all operations of the model.

Genetic Systems are a formalism inspired by genetic regulatory networks, suitable for modeling the interactions between genes and proteins, acting as regulatory products. The evolution is driven by genetic gates: a new object (representing a protein) is produced when all activator objects are available in the system, and no inhibitor object is present. Activators are not consumed by the application of such a rule. Objects disappear because of degradation: each object is equipped with a lifetime, and the object decays when such a lifetime expires.

We investigate the computational expressiveness of Genetic Systems with interleaving semantics (a single action is executed in a computational step): we show that they are Turing equivalent by providing a deterministic encoding of Random Access Machines in Genetic Systems. We also show that the computational power strictly decreases when moving to Genetic Systems where either the degradation or the inhibition mechanism are absent.

We give a classification of block-wise symmetric signatures in the theory of matchgate computations. The main proof technique is matchgate identities, a.k.a. useful Grassmann-Plücker identities.

We consider standard algorithms of finite graph theory, like for instance shortest path algorithms. We present two general methods to polynomially extend these algorithms to infinite graphs generated by deterministic graph grammars.

We show that the size reduction problem for fuzzy automata is related to the problem of solving a particular system of fuzzy relation equations. This system consists of infinitely many equations, and finding its general solution is a very difficult task, so we first consider one of its special cases, a finite system whose solutions, called right invariant fuzzy equivalences, are common generalizations of recently studied right invariant or well-behaved equivalences on NFAs, and congruences on fuzzy automata. We give a procedure for constructing the greatest right invariant fuzzy equivalence contained in a given fuzzy equivalence, which work if the underlying structure of truth values is a locally finite residuated lattice.

The theorem of shows the existence of nested factorisations — a la Ramsey — for finite words. This theorem has important applications in semigroup theory, and beyond.

We provide two improvements to the standard result. First we improve on all previously known bounds for the standard theorem. Second, we extend it to every ‘complete linear ordering’. We use this variant in a simplified proof of complementation of automata over words of countable scattered domain.