Abstract
We show that the directed st-connectivity problem cannot be expressed in symmetric Datalog, a fragment of Datalog introduced in [5]. It was shown there that symmetric Datalog programs can be evaluated in logarithmic space and that this fragment of Datalog captures logspace when augmented with negation, and an auxiliary successor relation S together with two constant symbols for the smallest and largest elements with respect to S. In contrast, undirected st-connectivity is expressible in symmetric Datalog and is in fact one of the simplest examples of the expressive power of this logic. It follows that undirected non-st-connectivity can be expressed in restricted symmetric monotone Krom \(\operatorname{SNP}\), whereas directed non-st-connectivity is only definable in the more expressive restricted monotone Krom \(\operatorname{SNP}\). By results of [8], the inexpressibility result for directed st-connectivity extends to a wide class of homomorphism problems that fail to meet a certain algebraic condition.
Research supported in part by NSERC, FQRNT and CRM.
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Egri, L., Larose, B., Tesson, P. (2008). Directed st-Connectivity Is Not Expressible in Symmetric Datalog. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70583-3_15
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DOI: https://doi.org/10.1007/978-3-540-70583-3_15
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