Related papers: Symbolic Representation of Algorithmic Game Semant…
We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…
Probabilistic omega-automata are variants of nondeterministic automata for infinite words where all choices are resolved by probabilistic distributions. Acceptance of an infinite input word can be defined in different ways: by requiring…
This work is a mathematician's attempt to understand intuitionistic logic. It can be read in two ways: as a research paper interspersed with lengthy digressions into rethinking of standard material; or as an elementary (but highly…
A large branch of explainable machine learning is grounded in cooperative game theory. However, research indicates that game-theoretic explanations may mislead or be hard to interpret. We argue that often there is a critical mismatch…
This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…
$\omega$-regular energy games, which are weighted two-player turn-based games with the quantitative objective to keep the energy levels non-negative, have been used in the context of verification and synthesis. The logic of modal…
Word sense disambiguation is a fundamental challenge in natural language understanding. Current methods are primarily aimed at coarse-grained representations (e.g. WordNet synsets or FrameNet frames) and require hand-annotated training data…
We investigate the expressive power of regular expressions for languages of countable words and establish their expressive equivalence with logical and algebraic characterizations. Our goal is to extend the classical theory of regular…
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…
Many problems can be viewed as games, where one or more agents try to ensure that certain objectives hold no matter the behavior from the environment and other agents. In recent years, a number of logical formalisms have been proposed for…
We integrate foundational theories of meaning with a mathematical formalism of artificial general intelligence (AGI) to offer a comprehensive mechanistic explanation of meaning, communication, and symbol emergence. This synthesis holds…
Two-player (antagonistic) games on (possibly stochastic) graphs are a prevalent model in theoretical computer science, notably as a framework for reactive synthesis. Optimal strategies may require randomisation when dealing with inherently…
We study a game for recognising formal languages, in which two players with imperfect information need to coordinate on a common decision, given private input words correlated by a finite graph. The players have a joint objective to avoid…
Stochastic games are a convenient formalism for modelling systems that comprise rational agents competing or collaborating within uncertain environments. Probabilistic model checking techniques for this class of models allow us to formally…
Natural language provides an accessible and expressive interface to specify long-term tasks for robotic agents. However, non-experts are likely to specify such tasks with high-level instructions, which abstract over specific robot actions…
Semantic parsing converts natural language queries into structured logical forms. The paucity of annotated training samples is a fundamental challenge in this field. In this work, we develop a semantic parsing framework with the dual…
We introduced a family of infinite graphs directly associated with a class of von Neumann automaton model A_{G}. These are finite state models used in symbolic dynamics: stimuli models and in control theory. In the context of groupoid von…
In this paper we examine different meaning representations that are commonly used in different natural language applications today and discuss their limits, both in terms of the aspects of the natural language meaning they are modelling and…
We explore language semantics for automata combining probabilistic and nondeterministic behavior. We first show that there are precisely two natural semantics for probabilistic automata with nondeterminism. For both choices, we show that…