Computing and Combinatorics: 16th Annual International by Manuel Blum (auth.), My T. Thai, Sartaj Sahni (eds.)

By Manuel Blum (auth.), My T. Thai, Sartaj Sahni (eds.)

This ebook constitutes the complaints of the sixteenth Annual overseas convention on Computing and Combinatorics, held in Nha Trang, Vietnam, in July 2010.

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ICALP 2009. LNCS, vol. 5555, pp. 378–389. Springer, Heidelberg (2009) 12. : Vertex and edge covers with clustering properties: Complexity and algorithms. Journal of Discrete Algorithms 7, 149–167 (2009) 13. : Parameterized Complexity Theory. In: Texts in Theoretical Computer Science. An EATCS Series, Springer, Heidelberg (2006) 14. : Subexponential algorithms for partial cover problems. N. ) IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2009).

Our results show that the difference between #BWBP and #NC1 is captured exactly by the addition of a visible stack to a nondeterministic finite-state automata. 1 Introduction We investigate the complexity of the following problem: Fix any visibly pushdown automata V . Given a word w over the input alphabet of V , compute the number of accepting paths that V has on w. We show that this problem is complete for the counting class #NC1 . The class #NC1 was first singled out for systematic study in [10], and has been studied from many different perspectives; see [1,5,7,10].

Proof: We show a finite process for changing PRST into QRST with the desired properties. Let H = {r | PR (r) > PR (r)} and let L = {r | PR (r) < PR (r)}. Until |H| = 0, fix some r ∈ H and r ∈ L and fix s, t such that PRST (r, s, t) > 0. Define, α := min{PRST (r, s, t), |PR (r) − PR (r)|, |PR (r ) − PR (r )|} and set PRST (r, s, t) := PRST (r, s, t) − α and PRST (r , s, t) := PRST (r , s, t) + α. The process only decreases PR − PR and therefore Condition 1 holds. By definition, we continue the process until Condition 2 holds.

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