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In this paper, we first study the conversion of weighted two-way automata to one-way automata. We show that this conversion preserves the unambiguity but does not preserve the determinism. Yet, we prove that the conversion of an unambiguous…
A classical approach to formal policy synthesis in stochastic dynamical systems is to construct a finite-state abstraction, often represented as a Markov decision process (MDP). The correctness of these approaches hinges on a behavioural…
In recent years, machine learning (ML) has gained significant popularity in the field of chemical informatics and electronic structure theory. These techniques often require researchers to engineer abstract "features" that encode chemical…
A process algebra is proposed, whose semantics maps a term to a nondeterministic finite automaton (NFA, for short). We prove a representability theorem: for each NFA $N$, there exists a process algebraic term $p$ such that its semantics is…
Symbolic computation is an important approach in automated program analysis. Most state-of-the-art tools perform symbolic computation as interpreters and directly maintain symbolic data. In this paper, we show that it is feasible, and in…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
The hard problem in artificial intelligence asks how the shuffling of syntactical symbols in a program can lead to systems which experience semantics and qualia. We address this question in three stages. First, we introduce a new class of…
We give an unique string representation, up to isomorphism, for initially connected deterministic finite automata (ICDFAs) with n states over an alphabet of k symbols. We show how to generate all these strings for each n and k, and how its…
Controllers for autonomous robotic systems can be specified using state machines. However, these are typically developed in an ad hoc manner without formal semantics, which makes it difficult to analyse the controller. Simulations are often…
Some effects are considered to be higher-level than others. High-level effects provide expressive and succinct abstraction of programming concepts, while low-level effects allow more fine-grained control over program execution and…
There are many types of automata and grammar models that have been studied in the literature, and for these models, it is common to determine whether certain problems are decidable. One problem that has been difficult to answer throughout…
Many of the numerous automaton models proposed in the literature can be regarded as a finite automaton equipped with an additional storage mechanism. In this thesis, we focus on two such models, namely the finite automata over groups and…
Visual analytics systems combine machine learning or other analytic techniques with interactive data visualization to promote sensemaking and analytical reasoning. It is through such techniques that people can make sense of large, complex…
In automata theory, while determinisation provides a standard route to solving many common problems in automata theory, some weak forms of nondeterminism can be dealt with in some problems without costly determinisation. For example, the…
Transformers are ubiquitous models in the natural language processing (NLP) community and have shown impressive empirical successes in the past few years. However, little is understood about how they reason and the limits of their…
We study three notions of directability of fuzzy automata akin to the D1-, D2- and D3-directability of nondeterministic automata. Thus an input word $w$ of a fuzzy automaton is D1-directing if a fixed single state is reachable by $w$ from…
Formal/symbolic semantics can provide canonical, rigid controllability and interpretability to sentence representations due to their \textit{localisation} or \textit{composition} property. How can we deliver such property to the current…
Classic control techniques typically rely on a model of the system's response to external inputs, which is difficult to obtain from first principles especially if the unknown dynamics are nonlinear. In this paper, we address this issue by…
Imitation learning frameworks for robotic manipulation have drawn attention in the recent development of language model grounded robotics. However, the success of the frameworks largely depends on the coverage of the demonstration cases:…
The control of robots for manipulation tasks generally relies on visual input. Recent advances in vision-language models (VLMs) enable the use of natural language instructions to condition visual input and control robots in a wider range of…