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- W1529356409 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 Stogether 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." @default.
- W1529356409 created "2016-06-24" @default.
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- W1529356409 date "2008-08-12" @default.
- W1529356409 modified "2023-10-18" @default.
- W1529356409 title "Directed st-Connectivity Is Not Expressible in Symmetric Datalog" @default.
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- W1529356409 doi "https://doi.org/10.1007/978-3-540-70583-3_15" @default.
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