Related papers: On Causal Equivalence by Tracing in String Rewriti…
Cyclic words are equivalence classes of cyclic permutations of ordinary words. When a group is given by a rewriting relation, a rewriting system on cyclic words is induced, which is used to construct algorithms to find minimal length…
Discrete statistical models supported on labelled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the…
String diagrams are a powerful tool for reasoning about composite structures in symmetric monoidal categories. By representing string diagrams as graphs, equational reasoning can be done automatically by double-pushout rewriting. !-graphs…
We show that, when the actions of a Mazurkiewicz trace are considered not merely as atomic (i.e., mere names) but transformations from a specified type of inputs to a specified type of outputs, we obtain a novel notion of presentation for…
The aim of this paper is to discuss a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was…
Proofs by logical relations play a key role to establish rich properties such as normalization or contextual equivalence. They are also challenging to mechanize. In this paper, we describe the completeness proof of algorithmic equality for…
In the graphical calculus of planar string diagrams, equality is generated by exchange moves, which swap the heights of adjacent vertices. We show that left- and right-handed exchanges each give strongly normalizing rewrite strategies for…
Causal graphs, such as directed acyclic graphs (DAGs) and partial ancestral graphs (PAGs), represent causal relationships among variables in a model. Methods exist for learning DAGs and PAGs from data and for converting DAGs to PAGs.…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
We introduce a trace semantics for a call-by-value language with full polymorphism and higher-order references. This is an operational game semantics model based on a nominal interpretation of parametricity whereby polymorphic values are…
In this paper we have investigated enumeration orders of elements of r.e. sets enumerated by means of Turing machines. We have defined a reducibility based on enumeration orders named "Enumeration Order Reducibility" on computable functions…
The task of incomplete utterance rewriting has recently gotten much attention. Previous models struggled to extract information from the dialogue context, as evidenced by the low restoration scores. To address this issue, we propose a novel…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
We describe a mathematical framework for equational reasoning about infinite families of string diagrams which is amenable to computer automation. The framework is based on context-free families of string diagrams which we represent using…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…
We continue the investigation of tabular algebras with trace (a certain class of associative ${\Bbb Z}[v, v^{-1}]$-algebras equipped with distinguished bases) by determining the extent to which the tabular structure may be recovered from a…
We initiate the study of counting Markov Equivalence Classes (MEC) under logical constraints. MECs are equivalence classes of Directed Acyclic Graphs (DAGs) that encode the same conditional independence structure among the random variables…
Reverse Mathematics (RM for short) is a program in the foundations of mathematics with the aim of finding the minimal axioms required for proving theorems about countable and separable objects. RM usually takes place in second-order…
We consider the question of computing the distribution of a permutation statistics over restricted permutations via enumeration schemes. The restricted permutations are those avoiding sets of vincular patterns (which include both classical…