Related papers: Two theorems about the P versus NP problem

For a natural language problem that requires some non-trivial reasoning to solve, there are at least two ways to do it using a large language model (LLM). One is to ask it to solve it directly. The other is to use it to extract the facts…

Difference Logic (DL) is a fragment of linear arithmetics where atoms are constraints x+k <= y for variables x,y (ranging over Q or Z) and integer k. We study the complexity of deciding the truth of existential DL sentences. This problem…

This paper considers the complexity and properties of KLM-style preferential reasoning in the setting of propositional logic with team semantics and dependence atoms, also known as propositional dependence logic. Preferential team-based…

We study Turing machines that are allowed absolutely no space overhead. The only work space the machines have, beyond the fixed amount of memory implicit in their finite-state control, is that which they can create by cannibalizing the…

We study the decidability of termination for two CHR dialects which, similarly to the Datalog like languages, are defined by using a signature which does not allow function symbols (of arity >0). Both languages allow the use of the =…

In this paper, we interpret NDTM (NonDeterministic Turing Machine) used to define NP by tracing to the source of NP. Originally NP was defined as the class of problems solvable in polynomial time by a NDTM in the theorem of Cook, where the…

The class of Unambiguous Star-Free Regular Languages (UL) was defined by Schutzenberger as the class of languages defined by Unambiguous Polynomials. UL has been variously characterized (over finite words) by logics such as TL[X_a,Y_a],…

The main result is that for lambda strong limit singular failing the continuum hypothesis (i.e. 2^lambda > lambda^+), a polarized partition theorem holds.

The discreteness problem for finitely generated subgroups of $PSL(2,\mathbb{R})$ and $PSL(2,\mathbb{C})$ is a long-standing open problem. In this paper we consider whether or not this problem is decidable by an algorithm. Our main result is…

The question whether P equals NP revolves around the discrepancy between active production and mere verification by Turing machines. In this paper, we examine the analogous problem for finite transducers and automata. Every nondeterministic…

We consider a general class of decision problems concerning formal languages, called ``(one-dimensional) unboundedness predicates'', for automata that feature reversal-bounded counters (RBCA). We show that each problem in this class reduces…

It is undecidable whether the language recognized by a probabilistic finite automaton is empty. Several other undecidability results, in particular regarding problems about matrix products, are based on this important theorem. We present…

A regular language $L$ is said to be prime, if it is not the product of two non-trivial languages. Martens et al. settled the exact complexity of deciding primality for deterministic finite automata in 2010. For finite languages, Mateescu…

Results of computational complexity exist for a wide range of phrase structure-based grammar formalisms, while there is an apparent lack of such results for dependency-based formalisms. We here adapt a result on the complexity of…

This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…

Piecewise testable languages form the first level of the Straubing-Th\'erien hierarchy. The membership problem for this level is decidable and testing if the language of a DFA is piecewise testable is NL-complete. The question has not yet…

We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…

This paper introduces a generic framework that provides sufficient conditions for guaranteeing polynomial-time decidability of fixed-negation fragments of first-order theories that adhere to certain fixed-parameter tractability…

This paper continues the functional approach to the P-versus-NP problem, begun in [1]. Here we focus on the monoid RM_2^P of right-ideal morphisms of the free monoid, that have polynomial input balance and polynomial time-complexity. We…

Recently it was shown that it is undecidable whether a term rewrite system can be proved terminating by a polynomial interpretation in the natural numbers. In this paper we show that this is also the case when restricting the…