Related papers: Completeness Theorems for Pomset Languages and Con…
Simon's congruence $\sim_k$ is defined as follows: two words are $\sim_k$-equivalent if they have the same set of subsequences of length at most $k$. We propose an algorithm which computes, given two words $s$ and $t$, the largest $k$ for…
We consider the rational subset membership problem for Baumslag-Solitar groups. These groups form a prominent class in the area of algorithmic group theory, and they were recently identified as an obstacle for understanding the rational…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
We study a standard operator on classes of languages: unambiguous polynomial closure. We prove that for every class C of regular languages satisfying mild properties, the membership problem for its unambiguous polynomial closure UPol(C)…
We introduce a high-level language with Python-like syntax for string-to-string, polyregular, first-order definable transductions. This language features function calls, boolean variables, and nested for-loops. We devise and implement a…
Programs that combine I/O and countable probabilistic choice, modulo either bisimilarity or trace equivalence, can be seen as describing a probabilistic strategy. For well-founded programs, we might expect to axiomatize bisimilarity via a…
While pretrained language models (PLMs) primarily serve as general-purpose text encoders that can be fine-tuned for a wide variety of downstream tasks, recent work has shown that they can also be rewired to produce high-quality word…
We introduce a variant of de Bruijn words that we call perfect necklaces. Fix a finite alphabet. Recall that a word is a finite sequence of symbols in the alphabet and a circular word, or necklace, is the equivalence class of a word under…
Earlier an arbitrary poset $P$ was proved to be isomorphic to the collection of subsets of a space $M$ with two closures which are closed in the first closure and open in the other. As a space $M$ for this representation an algebraic dual…
We introduce OpSets, an executable framework for specifying and reasoning about the semantics of replicated datatypes that provide eventual consistency in a distributed system, and for mechanically verifying algorithms that implement these…
To Rogers (1994) we owe the insight that monadic second order predicate logic with multiple successors (MSO) is well suited in many respects as a realistic formal base for syntactic theorizing. However, the agreeable formal properties of…
We study a family of problems, called \prob{Maximum Solution}, where the objective is to maximise a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints. When the domain is Boolean…
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
We introduce Probabilistic Guarded Kleene Algebra with Tests (ProbGKAT), an extension of GKAT that allows reasoning about uninterpreted imperative programs with probabilistic branching. We give its operational semantics in terms of special…
We consider algebras of languages over the signature of reversible Kleene lattices, that is the regular operations (empty and unit languages, union, concatenation and Kleene star) together with intersection and mirror image. We provide a…
In this work we continue the syntactic study of completeness that began with the works of Immerman and Medina. In particular, we take a conjecture raised by Medina in his dissertation that says if a conjunction of a second-order and a…
The world's languages exhibit certain so-called typological or implicational universals; for example, Subject-Object-Verb (SOV) languages typically use postpositions. Explaining the source of such biases is a key goal of linguistics. We…