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Author Abiteboul, Serge ♦ Vardi, Moshe Y. ♦ Vianu, Victor
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1997
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Complexity classes ♦ Computational complexity ♦ Fixpoint logic ♦ Relational complexity
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 equally 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 use a theory of relational complexity, which bridges the 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 complexity classes. On the other hand, the expressive power of fixpoint logic can be precisely characterized in terms of relational complexity classes. This tight, three-way relationship among fixpoint logics, relational complexity and standard complexity yields in a uniform way logical analogs to all containments among the complexity classes P, NP, PSPACE, and EXPTIME. The logical formulation shows that some of the most tantalizing questions in complexity theory boil down to a single question: the relative power of inflationary vs. noninflationary 1st-order operators.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1997-01-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 44
Issue Number 1
Page Count 27
Starting Page 30
Ending Page 56


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Source: ACM Digital Library