Related papers: Considerations on P vs NP

Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…

Stephen Cook posited SAT is NP-Complete in 1971. If SAT is NP-Complete then, as is generally accepted, any polynomial solution of it must also present a polynomial solution of all NP decision problems. It is here argued, however, that NP is…

We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: (*) Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In…

The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the…

In this paper we investigate the intrinsic sequential time complexity of universal elimination procedures for arbitrary continuous data structures encoding input and output objects of elimination theory (i.e. polynomial equation systems)…

The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…

In this manuscript, we derive the principle of conservation of computational complexity. We measure computational complexity as the number of binary computations (decisions) required to solve a problem. Every problem then defines a unique…

Previously the author has demonstrated that a representative polynomial search partition is required to solve a NP-complete problem in deterministic polynomial time. It has also been demonstrated that finding such a partition can only be…

DPLL and resolution are two popular methods for solving the problem of propositional satisfiability. Rather than algorithms, they are families of algorithms, as their behavior depend on some choices they face during execution: DPLL depends…

In this paper we consider polynomial representability of functions defined over $Z_{p^n}$, where $p$ is a prime and $n$ is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to…

Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…

Motivated by the fact that information is encoded and processed by physical systems, the P versus NP problem is examined in terms of physical processes. In particular, we consider P as a class of deterministic, and NP as nondeterministic,…

Calculating the probability of an individual solution being selected under lexicase selection is an important problem in attempts to develop a deeper theoretical understanding of lexicase selection, a state-of-the art parent selection…

In this article, we deal with propositional calculi over a signature containing the classical implication $\to$ with the rules of modus ponens and substitution. For these calculi we consider few recognizing problems such as recognizing…

We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…

The Possible-Winner problem asks, given an election where the voters' preferences over the set of candidates is partially specified, whether a distinguished candidate can become a winner. In this work, we consider the computational…

Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…

We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…

We consider the thesis that an arithmetical relation, which holds for any, given, assignment of natural numbers to its free variables, is Turing-decidable if, and only if, it is the standard representation of a PA-provable formula. We show…

We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…