Light Affine Logic (LAL) is a logical system due to Girard and Asperti offering a polynomial time cut-elimination procedure. It can be used as a type system for lambda-calculus, ensuring a well-typed program has a polynomial time bound on any input. Types use modalities meant to control duplication. We consider parameterized types where parameters are on the number of modalities and the type in...

The ability to use a polynomial iterpretation to prove termination of a rewrite system naturally prompts the question as to what restriction on complexity this imposes. The main result of this paper is that a polynomial interpretation termination proof of a rewrite system R which computes a number theoretic function implies a polynomial bound on that function’s rate of growth.

We consider the two-variable interlace polynomial introduced by Arratia, Bollobás and Sorkin (2004). We develop two graph transformations which allow us to derive point-to-point reductions for the interlace polynomial. Exploiting these reductions we obtain new results concerning the computational complexity of evaluating the interlace polynomial at a fixed point. Regarding exact evaluation, we ...

(i) First we show that all the known algorithms for polynomial division can be represented as algorithms for triangular Toeplitz matrix inversion. In spite of the apparent difference of the algorithms of these two classes, their strong equivalence is demonstrated. (ii) Then we accelerate parallel division of two polynomials with integer coefficients of degrees at most m by a factor of log m com...

The general dimension is a combinatorial measure that characterizes the number of queries needed to learn a concept class. We use this notion to show that any p-evaluatable concept class with polynomial query complexity can be learned in polynomial time with the help of an oracle in the polynomial hierarchy, where the complexity of the required oracle depends on the query-types used by the lear...

An algorithm is designed which tests solvability of a system of k polynomial equations in n variables with degrees d within complexity polynomial in nd 3k . If a systems is solvable then the algorithm yields one of its solutions. Thus, for fixed d, k the complexity of the algorithm is polynomial.

In this article, we formalize polynomially bounded sequences that plays an important role in computational complexity theory. Class P is a fundamental computational complexity class that contains all polynomial-time decision problems [11], [12]. It takes polynomially bounded amount of computation time to solve polynomial-time decision problems by the deterministic Turing machine. Moreover we fo...

We study polynomial time complexity of type 2 functionals. For that purpose, we introduce a first order functional stream language. We give criteria, named well-founded, on such programs relying on second order interpretation that characterize two variants of type 2 polynomial complexity including the Basic Feasible Functions (BFF). These characterizations provide a new insight on the complexit...

This paper addresses the Tardy/Lost penalty minimization with common due dates on a single machine. According to this performance measure, if the tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. Initially, we present a 2-approximation algorithm and examine its worst case ratio bound. Then, a pseudo-polynomial dynamic programming algorithm is de...

In this paper we will survey some recent results on complexity theoretic model theory and algebra Essentially there are two major themes in this work The rst which we call complexity theoretic model theory deals with model ex istence questions For example given a recursive model A is there there a polynomial time exponential time polynomial space etc model B which is isomorphic to A The second ...