Related papers: A syntactical analysis of non-size-increasing poly…
We introduce syntactic restrictions of the lexicographic path ordering to obtain the Light Lexicographic Path Ordering. We show that the light lexicographic path ordering leads to a characterisation of the functions computable in space…
The authors of ``A note on the complexity of a phaseless polynomial interpolation'' have shown that phaseless polynomial interpolation over $\mathbf{Q}$ is possible with $n+2$ points, where $n$ is the upper-bound on the degree of a…
We consider the concept of a local set of inference rules. A local rule set can be automatically transformed into a rule set for which bottom-up evaluation terminates in polynomial time. The local-rule-set transformation gives…
In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…
A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…
The possibilities for limit functions on a Fatou component for the iteration of a single polynomial or rational function are well understood and quite restricted. In non-autonomous iteration, where one considers compositions of arbitrary…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
These notes contain, among others, a proof that the average running time of an easy solution to the satisfiability problem for propositional calculus is, under some reasonable assumptions, linear (with constant 2) in the size of the input.…
We propose an approach to determine the continual progression of algorithmic efficiency, as an alternative to standard calculations of time complexity, likely, but not exclusively, when dealing with data structures with unknown maximum…
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…
Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…
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…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the…
Girard's Light linear logic (LLL) characterized polynomial time in the proof-as-program paradigm with a bound on cut elimination. This logic relied on a stratification principle and a "one-door" principle which were generalized later…