Fixpoint Logics, Relational Machines, and Computational Complexity

Fixpoint Logics, Relational Machines, and Computational Complexity (1993)

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by Serge Abiteboul , Moshe Y. Vardi , Victor Vianu

Venue:	In Structure and Complexity
Citations:	33 - 5 self

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Datum	Value	Source
TITLE	Fixpoint Logics, Relational Machines, and Computational Complexity	user correction - Legacy Corrections
AUTHOR NAME	Serge Abiteboul	user correction - Legacy Corrections
AUTHOR AFFIL	INRIA, BP 105	user correction - Legacy Corrections
AUTHOR ADDR	78153 Le Chesnay CEDEX; France	user correction - Legacy Corrections
AUTHOR NAME	Moshe Y. Vardi	user correction - Legacy Corrections
AUTHOR AFFIL	IBM Almaden Research Center	user correction - Legacy Corrections
AUTHOR ADDR	San Jose, CA 95120-6099; USA	user correction - Legacy Corrections
AUTHOR NAME	Victor Vianu	user correction - Legacy Corrections
AUTHOR AFFIL	CSE C-0114 UC San Diego	user correction - Legacy Corrections
AUTHOR ADDR	La Jolla, CA 92093; USA	user correction - Legacy Corrections
ABSTRACT	We establish a general connection between fixpoint logic and complexity. On one side, we have fixpoint logic, parameterized by the choices of 1st-order operators (inflationary or noninflationary) and iteration constructs (deterministic, nondeterministic, or alternating). On the other side, we have the complexity classes between P and EXPTIME. Our parameterized fixpoint logics capture the complexity classes P, NP, PSPACE, and EXPTIME, but equality is achieved only over ordered structures. There is, however, an inherent mismatch between complexity and logic -- while computational devices work on encodings of problems, logic is applied directly to the underlying mathematical structures. To overcome this mismatch, we develop a theory of relational complexity, which bridges tha gap between standard complexity and fixpoint logic. On one hand, we show that questions about containments among standard complexity classes can be translated to questions about containments among relational complex...	user correction - Legacy Corrections
YEAR	1993	user correction - Legacy Corrections
VENUE	In Structure and Complexity	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	156--168	INFERENCE
VOLUME	44	INFERENCE
CITATIONS	46 found	ParsCit 1.0