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On constraint satisfaction problems below P.

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Title: On constraint satisfaction problems below P.
Authors: EGRI, LÁSZLÓ1 laszlo.egri@mail.mcgill.ca
Source: Journal of Logic & Computation. Jun2016, Vol. 26 Issue 3, p893-922. 30p.
Subjects: CSP (Computer program language), Datalog (Computer program language), Branching processes, Logic programming, Duality (Logic)
Abstract: Symmetric Datalog, a fragment of the logic programming language Datalog, is conjectured to capture all constraint satisfaction problems (CSP) in L. Therefore developing tools that help us understand whether or not a CSP can be defined in symmetric Datalog is an important task. It is widely known that a CSP is definable in Datalog and linear Datalog if and only if that CSP has bounded treewidth and bounded pathwidth duality, respectively. In the case of symmetric Datalog, Bulatov, Krokhin and Larose ask for such a duality (2008, Vol. 5250 of LNCS, 93-124). We provide two such dualities, and give applications. In particular, we give a short and simple new proof of the result of Dalmau and Larose that 'Maltsev + Datalog ⇒ symmetric Datalog' (2008, IEEE Symposium on LICS, 297-306). In the second part of the article, we provide some evidence for the conjecture of Dalmau (2002, Proc. ICALP, 414-425) that every CSP in NL is definable in linear Datalog. Our results also show that a wide class of CSPs-CSPs which do not have bounded pathwidth duality (e.g. the P-complete Horn-3Sat problem)-cannot be defined by any polynomial size family of monotone read-once non-deterministic branching programs. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="DE" term="%22CSP+%28Computer+program+language%29%22">CSP (Computer program language)</searchLink><br /><searchLink fieldCode="DE" term="%22Datalog+%28Computer+program+language%29%22">Datalog (Computer program language)</searchLink><br /><searchLink fieldCode="DE" term="%22Branching+processes%22">Branching processes</searchLink><br /><searchLink fieldCode="DE" term="%22Logic+programming%22">Logic programming</searchLink><br /><searchLink fieldCode="DE" term="%22Duality+%28Logic%29%22">Duality (Logic)</searchLink>
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  Data: Symmetric Datalog, a fragment of the logic programming language Datalog, is conjectured to capture all constraint satisfaction problems (CSP) in L. Therefore developing tools that help us understand whether or not a CSP can be defined in symmetric Datalog is an important task. It is widely known that a CSP is definable in Datalog and linear Datalog if and only if that CSP has bounded treewidth and bounded pathwidth duality, respectively. In the case of symmetric Datalog, Bulatov, Krokhin and Larose ask for such a duality (2008, Vol. 5250 of LNCS, 93-124). We provide two such dualities, and give applications. In particular, we give a short and simple new proof of the result of Dalmau and Larose that 'Maltsev + Datalog ⇒ symmetric Datalog' (2008, IEEE Symposium on LICS, 297-306). In the second part of the article, we provide some evidence for the conjecture of Dalmau (2002, Proc. ICALP, 414-425) that every CSP in NL is definable in linear Datalog. Our results also show that a wide class of CSPs-CSPs which do not have bounded pathwidth duality (e.g. the P-complete Horn-3Sat problem)-cannot be defined by any polynomial size family of monotone read-once non-deterministic branching programs. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1093/logcom/exu003
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        Text: English
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      – SubjectFull: Datalog (Computer program language)
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      – SubjectFull: Branching processes
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              Text: Jun2016
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