In this paper we show that several classes of languages from computational complexity theory, such as EXPTIME, can be characterized in a continuous manner by using only polynomial differential equations. This characterization applies not to languages, but also functions, the defining Grzegorczyk hierarchy, which implies an analog class elementary computable functions and primitive recursive fun...

We introduce a general concept of complexity and a polynomial type algebraic complexity of a polynomial mapping. The notion of polynomial type algebraic complexity encompasses the determinantal complexity. We analyze the relation between polynomial type algebraic complexities and elusive functions. We study geometric-algebraic properties of polynomial type computational complexities. We present...

Recently, motivated by the study of vectorized stream cipher systems, the joint linear complexity and joint minimal polynomial of multisequences have been investigated. Let S be a linear recurring sequence over finite field Fqm with minimal polynomial h(x) over Fqm. Since Fqm and F m q are isomorphic vector spaces over the finite field Fq, S is identified with an m-fold multisequence S over the...

The purpose of this paper is to present a polynomial time algorithm which determines the lot sizes for purchase component in Material Requirement Planning (MRP) environments with deterministic time-phased demand with zero lead time. In this model, backlog is not permitted, the unit purchasing price is based on the all-units discount system and resale of the excess units is possible at the order...

In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent...

We introduce a notion of a polynomial type complexity of a multivariate polynomial. We provide examples of polynomial type complexities, including the determinantal complexity. We present two algorithms (not very efficient) to construct test functions for lower bounds (or explicit obstructions) of a polynomial type complexity, one of them is based on Gröbner bases, the other uses the resultant ...

We present a new method for inferring complexity properties for imperative programs with bounded loops. The properties handled are: polynomial (or linear) boundedness of computed values, as a function of the input; and similarly for the running time. It is well known that complexity properties are undecidable for a Turing-complete programming language. Much work in program analysis overcomes th...

D. Grigoriev-G. Koshevoy recently proved that tropical Schur polynomials have (at worst) polynomial tropical semiring complexity. They also conjectured tropical skew Schur polynomials have at least exponential complexity; we establish a polynomial complexity upper bound. Our proof uses results about (stable) Schubert polynomials, due to R. P. Stanley and S. Billey-W. Jockusch-R. P. Stanley, tog...