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Kleene algebra with tests, KAT, provides a simple two-sorted algebraic framework for verifying properties of propositional while programs. Kleene algebra with domain, KAD, is a one-sorted alternative to KAT. The equational theory of KAT…
We analyzed the performance of a biologically inspired algorithm called the Corrected Projections Algorithm (CPA) when a sparseness constraint is required to unambiguously reconstruct an observed signal using atoms from an overcomplete…
Kleene Algebra with Tests (KAT) provides an elegant algebraic framework for describing non-deterministic finite-state computations. Using a small finite set of non-deterministic programming constructs (sequencing, non-deterministic choice,…
We introduce Symbolic Alternating Finite Automata (s-AFA) as an expressive, succinct, and decidable model for describing sets of finite sequences over arbitrary alphabets. Boolean operations over s-AFAs have linear complexity, which is in…
Alternating parity automata (APAs) provide a robust formalism for modelling infinite behaviours and play a central role in formal verification. Despite their widespread use, the algebraic theory underlying APAs has remained largely…
In Model-Based Systems Engineering (MBSE), the Systems Modeling Language (SysML) specification includes a metamodel that defines the language concepts and a user model that defines how the language concepts are represented. In SysML, an…
Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep…
We introduce a version of probabilistic Kleene algebra with angelic nondeterminism and a corresponding class of automata. Our approach implements semantics via distributions over multisets in order to overcome theoretical barriers arising…
The state-of-the-art pre-trained language representation models, such as Bidirectional Encoder Representations from Transformers (BERT), rarely incorporate commonsense knowledge or other knowledge explicitly. We propose a pre-training…
Existing formalisms for the algebraic specification and representation of networks of reversible agents suffer some shortcomings. Despite multiple attempts, reversible declensions of the Calculus of Communicating Systems (CCS) do not offer…
When faced with novel situations, people are able to marshal relevant considerations from a wide range of background knowledge and put these to use in inferences and predictions. What permits us to draw in globally relevant information and…
We present a reflexive tactic for deciding the equational theory of Kleene algebras in the Coq proof assistant. This tactic relies on a careful implementation of efficient finite automata algorithms, so that it solves casual equations…
Deep learning models perform poorly on tasks that require commonsense reasoning, which often necessitates some form of world-knowledge or reasoning over information not immediately present in the input. We collect human explanations for…
We present probabilistic arithmetic automata (PAAs), a general model to describe chains of operations whose operands depend on chance, along with two different algorithms to exactly calculate the distribution of the results obtained by such…
We study (bi)simulation-like preorder/equivalence checking on the class of visibly pushdown automata and its natural subclasses visibly BPA (Basic Process Algebra) and visibly one-counter automata. We describe generic methods for proving…
Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…
The theory of higher-dimensional automata (HDAs) has seen rapid progress in recent years, and first applications, notably to Petri net analysis, are starting to show. It has, however, emerged that HDAs themselves often are too strict a…
Chains of co-B\"uchi automata (COCOA) have recently been introduced as a new canonical model for representing arbitrary omega-regular languages. They can be minimized in polynomial time and are hence an attractive language representation…