On constraint satisfaction problems below P
László Egri · Journal of Logic and Computation · 2014
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 H orn -3S at problem)–cannot be defined by any polynomial size family of monotone read-once non-deterministic branching programs.