Related papers: Convergence and Diversity in the Control Hierarchy
This thesis concerns the implementation of Lambda Prolog, a higher-order logic programming language that supports the lambda-tree syntax approach to representing and manipulating formal syntactic objects. Lambda Prolog achieves its…
Formal language techniques have been used in the past to study autonomous dynamical systems. However, for controlled systems, new features are needed to distinguish between information generated by the system and input control. We show how…
Stone-type dualities provide a powerful mathematical framework for studying properties of logical systems. They have recently been fruitfully explored in understanding minimisation of various types of automata. In Bezhanishvili et al.…
Existing work on controlled text generation (CTG) assumes a control interface of categorical attributes. In this work, we propose a natural language (NL) interface, where we craft a PCFG to embed the control attributes into natural language…
Recently, a new paradigm was introduced in automata theory. The main idea is to classify regular languages according to their propensity to be sorted, establishing a deep connection between automata theory and data compression [J. ACM…
A directed acyclic graph (DAG) can represent a two-dimensional string or picture. We propose recognizing picture languages using DAG automata by encoding 2D inputs into DAGs. An encoding can be input-agnostic (based on input size only) or…
In this paper we show that an account for coordination can be constructed using the derivation structures in a lexicalized Tree Adjoining Grammar (LTAG). We present a notion of derivation in LTAGs that preserves the notion of fixed…
Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free…
We investigate parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity. We show that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog) enjoys…
The Turing machine models an old-fashioned computer, that does not interact with the user or with other computers, and only does batch processing. Therefore, we came up with a Reactive Turing Machine that does not have these shortcomings.…
Large Language Models (LLMs) have demonstrated impressive capabilities in complex reasoning tasks, yet they still struggle to reliably verify the correctness of their own outputs. Existing solutions to this verification challenge often…
Due to the works of S. Bozapalidis and A. Alexandrakis, there is a well-known characterization of recognizable weighted tree languages over fields in terms of finite-dimensionality of syntactic vector spaces. Here we prove a…
Despite extensive research both on the theoretical and practical fronts, formalising, reasoning about, and implementing languages with variable binding is still a daunting endeavour - repetitive boilerplate and the overly complicated…
Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator [18] was introduced to formalise programs running in parallel. In other direction, other authors proposed a systematic…
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…
We study weighted basic parallel processes (WBPP), a nonlinear recursive generalisation of weighted finite automata inspired from process algebra and Petri net theory. Our main result is an algorithm of 2-EXPSPACE complexity for the WBPP…
Let D denote an infinite alphabet -- a set that consists of infinitely many symbols. A word w = a_0 b_0 a_1 b_1 ... a_n b_n of even length over D can be viewed as a directed graph G_w whose vertices are the symbols that appear in w, and the…
In this paper, we present a derivative-based, functional recognizer and parser generator for visibly pushdown grammars. The generated parser accepts ambiguous grammars and produces a parse forest containing all valid parse trees for an…
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…
Despite the success of Large Language Models (LLMs) on various tasks following human instructions, controlling model generation at inference time poses a persistent challenge. In this paper, we introduce Ctrl-G, an adaptable framework that…