1. Introduction: The Classical Decision Problem.- 1.1 The Original Problem.- 1.2 The Transformation of the Classical Decision Problem.- 1.3 What Is and What Isn't in this Book.- I. Undecidable… Expand

We prove that the satisfiability problems for the guarded fragment ( GF ) and the loosely guarded fragment of first-order logic are complete for deterministic double exponential time.Expand

We study definability and complexity issues for automatic structures and prove that they are closed under finitary Feferman-Vaught-like products.Expand

We improve Mortimer's bound by one exponential and show that every satisfiable FO2-sentence has a model whose size is at most exponential in the size of the sentence.Expand

A central aim and ever-lasting dream of computer science is to put the development of hardware and software systems on a mathematical basis which is both firm and practical. Such a scientific… Expand

We introduce an atomic formula $${\vec{y} \bot_{\vec{x}} \vec{z}}$$ that gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence.Expand

We study definability problems and algorithmic issues for infinite structures that are finitely presented by automata or by model-theoretic interpretations.Expand