SIGACT news complexity theory column 49
ACM SIGACT News
The complexity of query containment in expressive fragments of XPath 2.0
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The complexity of query containment in expressive fragments of XPath 2.0
Journal of the ACM (JACM)
Model checking FO(R) over one-counter processes and beyond
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
On the relative succinctness of two extensions by definitions of multimodal logic
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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Succinctness is a natural measure for comparing the strength of different logics.Intuitively, a logic L驴 is more succinct than another logic L驴 if all properties that can be expressed in L驴 can be expressed in L驴 by formulas of (approximately) the same size, but some properties can be expressed in L驴 by (significantly) smaller formulas. We study the succinctness of logics on linear orders that have the same expressive power as first-order logic. Our first theorem is concerned with the finite variable fragments of first-order logic. We prove that: (i) Up to a polynomial factor, the 2- and the 3-variable fragments of first-order logic on linear orders have the same succinctness. (ii) The 4-variable fragment is exponentially more succinct than the 3-variable fragment. Our second main result compares the succinctness of first-order logic on linear orders with that of monadic second-order logic. We prove that the fragment of monadic second-order logic that has the same expressiveness as first-order logic on linear orders is non-elementarily more succinct than first-order logic.