We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: ⋆ Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In particular, we show that while (⋆) is doable in quantum randomized polynomial time when m=2 (and no classical randomized polynomial time algorithm is known), (⋆) i...

We analyze the complexity of Node Counting, a graph-traversal method. On many graphs arising in control problems in Artificial Intelligence, Node Counting performs as efficiently as other methods which are known to be of polynomial complexity in the number of states (e.g., Learning Real-Time A* method). We show that complexity of Node Counting on undirected graphs is (n p ), which is not polyno...

We show two sets of results applying the theory of extractors to resource-bounded Kolmogorov complexity: Most strings in easy sets have nearly optimal polynomial-time CD complexity. This extends work of Sipser Sip83] and Buhrman and Fortnow BF97]. We use extractors to extract the randomness of strings. In particular we show how to get from an arbitrary string, an incompressible string which enc...

Several variants of linear logic have been proposed to characterize complexity classes in the proofs-as-programs correspondence. Light linear logic (LLL) ensures a polynomial bound on reduction time, and characterizes in this way polynomial time (Ptime). In this paper we study the complexity of linear logic proof-nets and propose three semantic criteria based on context semantics: stratificatio...

Polynomial interpretations and their generalizations like quasi-interpretations have been used in the setting of first-order functional languages to design criteria ensuring statically some complexity bounds on programs [8]. This fits in the area of implicit computational complexity, which aims at giving machine-free characterizations of complexity classes. In this paper, we extend this approac...

We consider random instances of constraint satisfaction problems where each variable has domain size d, and each constraint contains t restrictions on k variables. For each (d; k; t) we determine whether the resolution complexity is a.s. constant, polynomial or exponential in the number of variables. For a particular range of (d; k; t), we determine a sharp threshold for resolution complexity w...

It is known that some polynomial Julia sets are algorithmically impossible to draw with arbitrary magnification. On the other hand, for a large class of examples the problem of drawing a picture has polynomial complexity. In this paper we demonstrate the existence of computable quadratic Julia sets whose computational complexity is arbitrarily high.

Abstract. This paper contributes to the study of Freely Rewriting Restarting Automata (FRR-automata) and Parallel Communicating Grammar Systems (PCGS), which both are useful models in computational linguistics. For PCGS we study two complexity measures called generation complexity and distribution complexity, and we prove that a PCGS Π , for which the generation complexity and the distribution ...