Reening Logical Characterizations of Advice Complexity Classes 1

Re ning Logical Characterizations of AdviceComplexity Classes 1

Numerical relations in logics are known to characterize, via the nite models of their sentences, polynomial advice nonuniform complexity classes. These are known to coincide with reduction classes of tally sets. Our contributions here are: 1/ a reenement of that characterization that individualizes the reduction class of each tally set, and 2/ characterizing logarithmic advice classes via numer...

Characterizations of Logarithmic Advice Complexity Classes

The complexity classes P=log and Full-P=log, corresponding to the two standard forms of logarithmic advice for polynomial time, are studied. The novel proof technique of \doubly exponential skip" is introduced, and characterizations for these classes are found in terms of several other concepts, among them easy-to-describe boolean circuits and reduction classes of tally sets with high regularit...

Logical Characterizations of Complexity Classes

A logical approach to locality in pictures languages

This paper deals with descriptive complexity of picture languages of any dimension by syntactical fragments of existential second-order logic. Two classical classes of picture languages are studied: The class of recognizable picture languages, i.e. projections of languages defined by local constraints (or tilings): it is known as the most robust class extending the class of regular languages to...

Resource analysis and implicit computational complexity

Implicit computational complexity (ICC) studies machine-independent approaches to computational complexity, with emphasis on approaches based on mathematical logic. Most work consists in characterizations of complexity classes by logical systems (via the Curry-Howard correspondence). Unfortunately, all these formal systems have been studied with different, often unrelated methodologies, and few...