Related papers: String Diagrammatic Trace Theory
We propose a new algebraic framework to discuss and classify recognizable tree languages, and to characterize interesting classes of such languages. Our algebraic tool, called preclones, encompasses the classical notion of syntactic…
These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…
We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
Characterisations theorems serve as important tools in model theory and can be used to assess and compare the expressive power of temporal languages used for the specification and verification of properties in formal methods. While complete…
Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…
We develop a theory of adjunctions in semigroup categories, i.e. monoidal categories without a unit object. We show that a rigid semigroup category is promonoidal, and thus one can naturally adjoin a unit object to it. This extends the…
We give a simpler proof using automata theory of a recent result of Kapovich, Weidmann and Myasnikov according to which so-called benign graphs of groups preserve decidability of the generalized word problem. These include graphs of groups…
We present graph-based translation models which translate source graphs into target strings. Source graphs are constructed from dependency trees with extra links so that non-syntactic phrases are connected. Inspired by phrase-based models,…
This study investigates the relationship between the phonological and morphological structure of Polish words and their meanings using Distributional Semantics. In the present analysis, we ask whether there is a relationship between the…
We introduce string diagrams for physical duoidal categories (normal $\otimes$-symmetric duoidal categories): they consist of string diagrams with wires forming a zigzag-free partial order and order-preserving nodes whose inputs and outputs…
For predual categories C and D we establish isomorphisms between opfibrations representing local varieties of languages in C, local pseudovarieties of D-monoids, and finitely generated profinite D-monoids. The global sections of these…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
We show that in any symmetric monoidal category, if a weight for colimits is absolute, then the resulting colimit of any diagram of dualizable objects is again dualizable. Moreover, in this case, if an endomorphism of the colimit is induced…
In category theory, the use of string diagrams is well known to aid in the intuitive understanding of certain concepts, particularly when dealing with adjunctions and monoidal categories. We show that string diagrams are also useful in…
A general overview of the phenomenon of automatic continuity of homomorphisms between Polish groups is given. In particular, we study variants and improvements of the closed graph theorem, applying these to the problem of continuity of…
Symmetric monoidal categories (SMCs) are a common framework for reasoning about computation, focusing on the parallel and sequential compositionality of operations. String diagrams are a ubiquitous and powerful tool for reasoning about…
We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result naturally introduces…
The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite rules, and to demonstrate that a logic can…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…