José L. Balcázar

Bi-immune sets for complexity classes

An infinite and co-infinite setA is bi-immune for a complexity classC if neitherA nor its complement has an infinite subset inC. We prove various equivalent characterizations of this notion. Also, we introduce a stronger version of bi-immunity and show how both notions relate to density and other properties of sets in EXPTIME.

Deciding bisimilarity isP-complete

In finite labelled transition systems the problems of deciding strong bisimilarity, observation equivalence and observation congruence areP-complete under many—oneNC-reducibility. As a consequence, algorithms for automated analysis of finite state systems based on bisimulation seem to be inherently sequential in the following sense: the design of anNC algorithm to solve any of these problems will require an algorithmic breakthrough, which is exceedingly hard to achieve.

Sparse sets lowness and highness

We develop the notions of “generalized lowness” for sets in PH (the union of the polynomial-time hierarchy) and of “generalized highness” for arbitrary sets. Also, we develop the notions of “extended lowness” and “extended highness” for arbitrary sets. These notions extend the decomposition of NP into low sets and high sets developed by Schoning [15] and studied by Ko and Schoning [9].We show that either every sparse set in PH is generalized high or no sparse set in PH is generalized high. Further, either every sparse set is extended high or no sparse set is extended high. In both situations, the former case corresponds to the polynomial-time hierarchy having only finitely many levels while the latter case corresponds to the polynomial-time hierarchy extending infinitely many levels.

Sets with small generalized Kolmogorov complexity

SummaryWe study the class of sets with small generalized Kolmogorov complexity. The following results are established: 1. A set has small generalized Kolmogorov complexity if and only if it is “semi-isomorphic” to a tally set. 2. The class of sets with small generalized Kolmogorov complexity is properly included in the class of “self-p-printable” sets. 3. The class of self-p-printable sets is properly included in the class of sets with “selfproducible circuits”. 4. A set S has self-producible circuits if and only if there is a tally set T such that P(T)=P(S). 5. If a set S has self-producible circuits, then NP(S)=NPB(S), where NPB( ) is the restriction of NP( ) studied by Book, Long, and Selman [4]. 6. If a set S is such that NP(S) =NPB(S), then NP(S)

Algorithms for Learning Finite Automata from Queries: A Unified View

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Computational power of neural networks: a characterization in terms of Kolmogorov complexity

P(S⊕SAT).

The Complexity of Graph Problems fore Succinctly Represented Graphs

New self-reducibility structures are proposed to deal with sets outside the class PSPACE and with sets in logarithmic space complexity classes. General properties derived from the definition are used to prove known results comparing uniform and nonuniform complexity classes and to obtain new ones regarding deterministic time classes, nondeterministic space classes, and reducibility to context-free languages.

Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules

In this survey we compare several known variants of the algorithm for learning deterministic finite automata via membership and equivalence queries. We believe that our presentation makes it easier to understand what is going on and what the differences between the various algorithms mean. We also include the comparative analysis of the algorithms, review some known lower bounds, prove a new one, and discuss the question of parallelizing this sort of algorithm.