Related papers: Specification and Automatic Verification of Comput…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
The verification of reductions, representative subsets of interleavings, simplifies correctness proofs of parameterized concurrent programs. We introduce an expressive class of syntactic reductions, which we call natural reductions. Natural…
We formally verify several computational reductions concerning the Post correspondence problem (PCP) using the proof assistant Coq. Our verifications include a reduction of a string rewriting problem generalising the halting problem for…
We distinguish finitarily between algorithmic verifiability, and algorithmic computability, to show that Goedel's 'formally' unprovable, but 'numeral-wise' provable, arithmetical proposition [(Ax)R(x)] can be finitarily evidenced as:…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
For a fixed marked surface $S$, we show that the problem of deciding whether or not a mapping class is reducible lies in $\textbf{NP}$. As usual this immediately gives an exponential time algorithm to decide whether or not a mapping class…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
The Graph Burning Problem (GBP) is a combinatorial optimization problem that has gained relevance as a tool for quantifying a graph's vulnerability to contagion. Although it is based on a very simple propagation model, its decision version…
State minimization of combinatorial filters is a fundamental problem that arises, for example, in building cheap, resource-efficient robots. But exact minimization is known to be NP-hard. This paper conducts a more nuanced analysis of this…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
For a fixed property (graph class) ${\Pi}$, given a graph G and an integer k, the ${\Pi}$-deletion problem consists in deciding if we can turn $G$ into a graph with the property ${\Pi}$ by deleting at most $k$ edges. The ${\Pi}$-deletion…
Commutativity has proven to be a powerful tool in reasoning about concurrent programs. Recent work has shown that a commutativity-based reduction of a program may admit simpler proofs than the program itself. The framework of…
The website reductions.network serves as a comprehensive database for exploring problems and reductions between them. It presents several complexity classes in the form of an interconnected graph where problems are represented as vertices,…
Program reductions are used widely to simplify reasoning about the correctness of concurrent and distributed programs. In this paper, we propose a general approach to proof simplification of concurrent programs based on exploring generic…
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…
In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set…
We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…
We present a performant and rigorous algorithm for certifying that a matrix is close to being a projection onto an irreducible subspace of a given group representation. This addresses a problem arising when one seeks solutions to…
Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…
In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…