Related papers: Efficient Computation by Three Counter Machines
We present efficient algorithms to decide whether two given counting functions on non-abelian free groups or monoids are at bounded distance from each other and to decide whether two given counting quasimorphisms on non-abelian free groups…
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…
It is well-known that one-tape Turing machines working in linear time are no more powerful than finite automata, namely they recognize exactly the class of regular languages. We prove that it is not decidable if a one-tape machine works in…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed correct after a time that is upper-bounded by a polynomial in the worst case. In an oracle setting, it is shown that such machines…
We survey results of a quarter century of work on computation by reversible general-purpose computers (in this setting Turing machines), and general reversible simulation of irreversible computations, with respect to energy-, time- and…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…
Suppose $P$ is a symmetric convex polygon in the plane. We give a polynomial time algorithm that decides if $P$ can tile the plane by transations at some level (not necessarily at level one; this is multiple tiling). The main technical…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some of the output variables are also input variables, linked by a linear dependency. Fundamental examples…
By using of analytical multi-logic expresses in conjunction with non-deterministic Turing machine the proposition was proved that algorithm of deterministic Turing counter machine of polynomial time complexity can be decreased to the…
In this paper, we present fast algorithms for the product of two multivariate polynomials in sparse representation. The bit complexity of our algorithms are studied in detail for various types of coefficients, and we derive new complexity…
This work formalizes efficient Fast Fourier-based multiplication algorithms for polynomials in quotient rings such as $\mathbb{Z}_{m}[x]/\left<x^{n}-a\right>$, with $n$ a power of 2 and $m$ a non necessarily prime integer. We also present a…
We present a deterministic polynomial-time algorithm that solves the 3-satisfiability problem.
We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time. Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where…
A syntactical proof is given that all functions definable in a certain affine linear typed lambda-calculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be…
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 discuss some claims that certain UCOMP devices can perform hypercomputation (compute Turing-uncomputable functions) or perform super-Turing computation (solve NP-complete problems in polynomial time). We discover that all these claims…
Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the…
Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factors, in particular vectorization, data movement and arithmetic…
We present polygraphic programs, a subclass of Albert Burroni's polygraphs, as a computational model, showing how these objects can be seen as first-order functional programs. We prove that the model is Turing complete. We use polygraphic…
We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one,…