相关论文: On the word problem for SP-categories, and the pro…

We solve the word problem for free double categories without equations between generators by translating it to the word problem for 2-categories. This yields a quadratic algorithm deciding the equality of diagrams in a free double category.…

We interpret several constructions with C*-algebras as colimits in the bicategory of correspondences. This includes crossed products for actions of groups and crossed modules, Cuntz-Pimsner algebras of proper product systems, direct sums…

This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationship between these classes and their connection with the…

We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent…

We study the language-theoretic aspects of the word problem, in the sense of Duncan & Gilman, of free products of semigroups and monoids. First, we provide algebraic tools for studying classes of languages known as super-AFLs, which…

Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…

Message passing is a key ingredient of concurrent programming. The purpose of this paper is to describe the equivalence between the proof theory, the categorical semantics, and term calculus of message passing. In order to achieve this we…

We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these…

It is proved that equalities between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equality in the language of free cartesian categories collapses a cartesian category into a preorder. An…

This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…

Neurosymbolic systems can satisfy logical constraints during learning without achieving the intended concept-label correspondence; this is a problem known as reasoning shortcuts. We formalize reasoning shortcuts as a constraint satisfaction…

We show that deciding whether an argument a is stronger than an argument b with respect to the discussion-based semantics of Amgoud and Ben-Naim is decidable in polynomial time. At its core, this problem is about deciding whether, for two…

(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…

We consider decision problems for relations over finite and infinite words defined by finite automata. We prove that the equivalence problem for binary deterministic rational relations over infinite words is undecidable in contrast to the…

Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…

In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…

A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…

Proof equivalence in a logic is the problem of deciding whether two proofs are equivalent modulo a set of permutation of rules that reflects the commutative conversions of its cut-elimination procedure. As such, it is related to the…

We study the freeness problem for matrix semigroups. We show that the freeness problem is decidable for upper-triangular $2\times 2$ matrices with rational entries when the products are restricted to certain bounded languages.

Just as conventional functional programs may be understood as proofs in an intuitionistic logic, so quantum processes can also be viewed as proofs in a suitable logic. We describe such a logic, the logic of compact closed categories and…