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The Classical Decision Problem
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. UndecidableExpand
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On The Restraining Power of Guards
  • E. Grädel
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1 December 1999
TLDR
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
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Automatic structures
TLDR
We study definability and complexity issues for automatic structures and prove that they are closed under finitary Feferman-Vaught-like products. Expand
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On the decision problem for two-variable first-order logic
TLDR
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
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Automata logics, and infinite games: a guide to current research
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 scientificExpand
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Dependence and Independence
TLDR
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
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Guarded fixed point logic
TLDR
We prove that the satisfiability problems for guarded fixed point logics are decidable and complete for deterministic double exponential time. Expand
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Finite Model Theory and Its Applications
TLDR
Unifying Themes in Finite Model Theory.- On the Expressive Power of Logics on Finite Models. Expand
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Finite Presentations of Infinite Structures: Automata and Interpretations
TLDR
We study definability problems and algorithmic issues for infinite structures that are finitely presented by automata or by model-theoretic interpretations. Expand
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Automata Logics, and Infinite Games
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