Related papers: Two theorems about the P versus NP problem

We study the language-theoretic properties of the word problem, in the sense of Duncan & Gilman, of weakly compressible monoids, as defined by Adian & Oganesian. We show that if $\mathcal{C}$ is a reversal-closed super-$\operatorname{AFL}$,…

Suppose that $P$ is a forcing notion, $L$ is a language (in $V$), $\dot{\tau}$ a $P$-name such that $P\Vdash$ "$\dot{\tau}$ is a countable $L$-structure". In the product $P\times P$, there are names $\dot{\tau_{1}},\dot{\tau_{2}}$ such that…

How predictable a word is can be quantified in two ways: using human responses to the cloze task or using probabilities from language models (LMs).When used as predictors of processing effort, LM probabilities outperform probabilities…

This paper investigates the reliability of explanations generated by large language models (LLMs) when prompted to explain their previous output. We evaluate two kinds of such self-explanations - extractive and counterfactual - using three…

I introduce an approach for automated reasoning in first order set theories that are not finitely axiomatizable, such as $ZFC$, and describe its implementation alongside the automated theorem proving software E. I then compare the results…

Let $R$ be a commutative integral unital domain and $L$ a free non-commutative Lie algebra over $R$. In this paper we show that the ring $R$ and its action on $L$ are 0-interpretable in $L$, viewed as a ring with the standard ring language…

Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. We present and discuss the separation problem…

ZFC has sentences that quantify over all sets or all ordinals, without restriction. Some have argued that sentences of this kind lack a determinate meaning. We propose a set theory called TOPS, using Natural Deduction, that avoids this…

We consider the following practical question: given a finite algebra A in a finite language, can we efficiently decide whether the variety generated by A has a difference term? We answer this question (positively) in the idempotent case and…

We show there exists a complete theory in a language of size continuum possessing a unique atomic model which is not constructible. We also show it is consistent with $ZFC + \aleph_1 < 2^{\aleph_0}$ that there is a complete theory in a…

The Curry-Howard correspondence is often called the proofs-as-programs result. I offer a generalization of this result, something which may be called machines as programs. Utilizing this insight, I introduce two new Turing Machines called…

We investigate two problems for a class C of regular word languages. The C-membership problem asks for an algorithm to decide whether an input language belongs to C. The C-separation problem asks for an algorithm that, given as input two…

We show that the polymodal provability logic GLP, in a language with at least two modalities and one variable, has nullary unification type. More specifically, we show that the formula [1]p does not have maximal unifiers, and exhibit an…

Given a class C of word languages, the C-separation problem asks for an algorithm that, given as input two regular languages, decides whether there exists a third language in C containing the first language, while being disjoint from the…

We prove the decidability for a class of languages which extend BST and NP-completeness for a subclass of them. The languages BST extended with unordered cartesian product, BST extended with ordered cartesian product and BST extended with…

We prove that language equivalence of deterministic one-counter automata is NL-complete. This improves the superpolynomial time complexity upper bound shown by Valiant and Paterson in 1975. Our main contribution is to prove that two…

This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…

This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a…

*by a standard (one-tape) Turing machine. It is well-known that the word problem for hyperbolic groups, whence in particular for free groups, can be solved in linear time. However, these algorithms run on machines more complicated than a…

The following problem is shown undecidable: given regular languages L,K of finite trees, decide if there exists a deterministic tree-walking automaton which accepts all trees in L and rejects all trees in K. The proof uses a technique of…