We define the BQS-UCmodel, a variant of the UCmodel, that deals with protocols in the bounded quantum storage model. We present a statistically secure commitment protocol in the BQS-UC model that composes concurrently with other protocols and an (a-priori) polynomially-bounded number of instances of itself. Our protocol has an efficient simulator which is important if one wishes to compose our ...

We consider continuous-time random walks with bounded jumps but unbounded rates (they depend polynomially on coordinates in the orthant). In applications, the case when the rates are bounded corresponds in applications to queueing theory, more precisely, to Markovian communication networks. The goal of this paper is to discuss the situation for polynomial rates; we show that the boundaries ofte...

In this paper, we extend the weak r -net theorem to a kinetic setting where the underlying set of points is moving polynomially with bounded description complexity. We establish that one can find a kinetic analog N of a weak r -net of cardinality O(r d(d+1) 2 log r) whose points are moving with coordinates that are rational functions with bounded description complexity. Moreover, each member of...

We consider optimization problems on weighted graphs where vertex and edge weights are polynomial functions of a parameter . We show that, if a problem satis es certain regularity properties and the underlying graph has bounded tree-width, the number of changes in the optimum solution is polynomially bounded. We also show that the description of the sequence of optimum solutions can be construc...

We present O(n’R + n3R3) time algorithms to compute the treewidth, pathwidth, minimum fill-in and minimum interval graph completion of asteroidal triple-free graphs, where n is the number of vertices and R is the number of minimal separators of the input graph. This yields polynomial time algorithms for the four NP-complete graph problems on any subclass of the asteroidal triple-free graphs tha...

Motivated by strong Karp-Lipton collapse results in bounded arithmetic, Cook and Kraj́ıček [1] have recently introduced the notion of propositional proof systems with advice. In this paper we investigate the following question: Given a language L, do there exist polynomially bounded proof systems with advice for L? Depending on the complexity of the underlying language L and the amount and type ...

The maximum common connected edge subgraph problem is to find a connected graph with the maximum number of edges that is isomorphic to a subgraph of each of the two input graphs, where it has applications in pattern recognition and chemistry. This paper presents a dynamic programming algorithm for the problem when the two input graphs are outerplanar graphs of a bounded vertex degree, where it ...

If one modifies the laws of Quantum Mechanics to allow nonlinear evolution of quantum states, this paper shows that NP-complete problems would be efficiently solvable in polynomial time with bounded probability (NP in BQP). With that (admittedly very unlikely) assumption, this is demonstrated by describing a polynomially large network of quantum gates that solves the 3SAT problem with bounded p...

In this paper, we extend the weak r -net theorem to a kinetic setting where the underlying set of points is moving polynomially with bounded description complexity. We establish that one can find a kinetic analog N of a weak r -net of cardinality O(r d(d+1) 2 log r) whose points are moving with coordinates that are rational functions with bounded description complexity. Moreover, each member of...

Notions of unambiguity for uniform circuits and AuxPDAs are studied and related to each other. In particular, a coincidence for counting and unambiguous versions of AuxPDAs and semi-unbounded fan-in circuits is shown. Moreover, an improved simulation of LOGUCFL (the class of languages logspace many-one reducible to unambiguous context-free languages) by unambiguous circuits and AuxPDAs is devel...