This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running times of oracle Turing machines and avoiding secondorder polynomials, which are notoriously difficult to handle. Furthermore, all machines that witness this st...

Levin introduced an average case complexity measure based on a notion of polynomial on average and de ned average case polynomial time many one reducibility among randomized decision problems We generalize his notions of average case complexity classes Random NP and Average P Ben David et al use the notation of hC Fi to denote the set of randomized de cision problems L such that L is a set in C...

Various algorithms connected with the computation of the minimal polynomial of a square n n matrix over a eld K are presented here. The complexity of the rst algorithm, where the complete factorization of the characteristic polynomial is needed, is O(p nn 3). It produces the minimal polynomial and all characteristic subspaces of a matrix of size n. Furthermore an iterative algorithm for the min...

Various algorithms connected with the computation of the minimal polynomial of a square n×n matrix over a field k are presented here. The complexity of the first algorithm, where the complete factorization of the characteristic polynomial is needed, is O( √ nn). It produces the minimal polynomial and all characteristic subspaces of a matrix of size n. Furthermore an iterative algorithm for the ...

We study the relations between the notions of highness, lowness and logical depth in the setting of complexity theory. We introduce a new notion of polynomial depth based on time bounded Kolmogorov complexity. We show our polynomial depth notion satisfies all basic logical depth properties, namely neither sets in P nor sets random for EXP are polynomial deep, and only polynomial deep sets can p...

We study the complexity of computation of a tropical Schur polynomial Tsλ where λ is a partition, and of a tropical polynomial Tmλ obtained by the tropicalization of the monomial symmetric function mλ. Then Tsλ and Tmλ coincide as tropical functions (so, as convex piece-wise linear functions), while differ as tropical polynomials. We prove the following bounds on the complexity of computing ove...

Dickenstein, A., N. Fitchas, M. Giusti and C. Sessa, The membership problem for unmixed polynomial ideals is solvable in single exponential time, Discrete Applied Mathematics 33 (1991) 73-94. Deciding membership for polynomial ideals represents a classical problem of computational commutative algebra which is exponential space hard. This means that the usual al membership problem which are base...

In this paper we present a new termination proof and complexity analysis of unfolding graph rewriting which is a specific kind of infinite graph rewriting expressing the general form of safe recursion. We introduce a termination order over sequences of terms together with an interpretation of term graphs into sequences of terms. Unfolding graph rewrite rules expressing general safe recursion ca...

Using ideas and results from polynomial approximation and exact computation we design approximation algorithms for several NP-hard combinatorial problems achieving ratios that cannot be achieved in polynomial time (unless a very unlikely complexity conjecture is confirmed) with worst-case complexity much lower (though super-polynomial) than that of an exact computation. We study in particular m...