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Finite automata (FA) are a fundamental computational abstraction that is widely used in practice for various tasks in computer science, linguistics, biology, electrical engineering, and artificial intelligence. Given an input word, an FA…
A rationally dynamically algebraic (RDA) power series is one that arises as (a component of) the solution of a system of differential equations of the form $\boldsymbol{y}' = F(\boldsymbol{y})$, where $F$ is a vector of rational functions…
Many tasks can be composed from a few independent components. This gives rise to a combinatorial explosion of possible tasks, only some of which might be encountered during training. Under what circumstances can transformers compositionally…
The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this…
Partially ordered automata are automata where the transition relation induces a partial order on states. The expressive power of partially ordered automata is closely related to the expressivity of fragments of first-order logic on finite…
A key feature of human intelligence is the ability to generalize beyond the training distribution, for instance, parsing longer sentences than seen in the past. Currently, deep neural networks struggle to generalize robustly to such shifts…
In this paper we regard languages and their acceptors -- such as deterministic or weighted automata, transducers, or monoids -- as functors from input categories that specify the type of the languages and of the machines to categories that…
A nondeterministic automaton is semantically deterministic (SD) if different nondeterministic choices in the automaton lead to equivalent states. Semantic determinism is interesting as it is a natural relaxation of determinism, and as some…
Data driven approaches for decision making applied to automated driving require appropriate generalization strategies, to ensure applicability to the world's variability. Current approaches either do not generalize well beyond the training…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
A word automaton recognizing a language $L$ is good for games (GFG) if its composition with any game with winning condition $L$ preserves the game's winner. While all deterministic automata are GFG, some nondeterministic automata are not.…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
Timed transition systems are behavioural models that include an explicit treatment of time flow and are used to formalise the semantics of several foundational process calculi and automata. Despite their relevance, a general mathematical…
Complementation and determinization are two fundamental notions in automata theory. The close relationship between the two has been well observed in the literature. In the case of nondeterministic finite automata on finite words (NFA),…
Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages,…
Analogous to regular string and tree languages, regular languages of directed acyclic graphs (DAGs) are defined in the literature. Although called regular, those DAG-languages are more powerful and, consequently, standard problems have a…
Regular expressions are commonly understood in terms of their denotational semantics, that is, through formal languages -- the regular languages. This view is inductive in nature: two primitives are equivalent if they are constructed in the…
This paper describes an architecture for robots that combines the complementary strengths of probabilistic graphical models and declarative programming to represent and reason with logic-based and probabilistic descriptions of uncertainty…
Compositionality -- the ability to combine familiar units like words into novel phrases and sentences -- has been the focus of intense interest in artificial intelligence in recent years. To test compositional generalization in semantic…
We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…