Fixpoint Logics, Relational Machines, and Computational Complexity

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dc.contributor.authorAbiteboul, Sergeen_US
dc.contributor.authorVardi, Moshe Y.en_US
dc.contributor.authorVianu, Victoren_US
dc.date.accessioned2017-08-02T22:03:29Zen_US
dc.date.available2017-08-02T22:03:29Zen_US
dc.date.issued1996-10-11en_US
dc.date.noteOctober 11, 1996en_US
dc.description.abstractWe 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 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.en_US
dc.format.extent30 ppen_US
dc.identifier.citationAbiteboul, Serge, Vardi, Moshe Y. and Vianu, Victor. "Fixpoint Logics, Relational Machines, and Computational Complexity." (1996) https://hdl.handle.net/1911/96458.en_US
dc.identifier.digitalTR96-265en_US
dc.identifier.urihttps://hdl.handle.net/1911/96458en_US
dc.language.isoengen_US
dc.rightsYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, but this permission is only for a period of forty-five (45) days from the most recent time that you verified that this technical report is still available from the Computer Science Department of Rice University under terms that include this permission. All other rights are reserved by the author(s).en_US
dc.titleFixpoint Logics, Relational Machines, and Computational Complexityen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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