Computer Science
Deciding periodicity of infinite words generated by morphisms is a classical result in combinatorics on words from 80's by Harju, Linna and Pansiot. In this paper, we are interested in this question in the abelian setting. Two words are…
Given a connected graph $G$ and a terminal set $R \subseteq V(G)$, the minimum Steiner tree problem (ST) asks for a tree that spans all of $R$ with at most $r$ vertices from $V(G)\backslash R$, for some integer $r\geq 0$. A \emph{split…
We study the observation congruences induced by rational polyhedral cones on vector-valued quantitative languages. The extreme rays of the dual cone define intrinsic covectors, and these covectors classify every incremental residual future…
Quantitative automata (QAs) extend finite-state automata on infinite words with weighted transitions to specify quantitative system properties. However, their finite weight sets rule out properties like average response time, where response…
Mathematical programming is widely employed across various sectors - such as logistics, energy, and workforce planning - to model and solve industrial optimisation problems, but its use requires substantial domain expertise. Large language…
The application of program transformation and algebraic methods to the development of efficient combinatorial optimization (CO) algorithms relies on an exhaustive combinatorial generator for the problem specification, followed by the fusion…
A suffixient set is a novel combinatorial object that captures the essential information of repetitive strings in a way that, provided with a random access mechanism, supports various forms of pattern matching. In this paper, we study the…
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…
Effective code optimization in compilers is crucial for computer and software engineering. The success of these optimizations primarily depends on the selection and ordering of the optimization passes applied to the code. While most…
Modern equality saturation systems excel at expression-level rewrites by exploring large spaces of equivalent programs without suffering from the phase-ordering problem. How- ever, these systems struggle to represent equivalence directly…
Markdown skill libraries for LLM agents ship as free-form prose, forcing the agent to re-derive both the input schema and the concrete invocation syntax on every retrieval. We observe that this often produces a "confused -> re-retrieve ->…
Despite rapid progress in LLM-based code generation, existing models are predominantly trained on imperative languages, leaving functional programming languages (FPLs) such as Haskell, OCaml, and Scala chronically underexplored, with even…
Specification synthesis, the task of automatically inferring formal specifications from program implementations and natural language, is important for refactoring, transpilation, optimization, and verification, yet remains an open challenge…
We describe a history-deterministic B\"uchi automaton that has strictly less states than every language-equivalent deterministic B\"uchi automaton. This solves a problem that had been open since the introduction of history-determinism and…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Given a finite and non-empty set $X$ and randomly selected specific functions and relations on $X$, we investigate the existence and non-existence of fixed points and reflexive points, respectively. First, we consider the class of…
History-determinism is a restricted notion of nondeterminism in automata, where the nondeterminism can be successfully resolved based solely on the prefix read so far. History-deterministic automata still allow for exponential succinctness…
History-deterministic automata are a restricted class of nondeterministic automata where the nondeterminism while reading an input can be resolved successfully based on the prefix read so far. History-deterministic automata are…
We consider $d$-dimensional configurations, that is, colorings of the $d$-dimensional integer grid $\mathbb{Z}^d$ with finitely many colors. Moreover, we interpret the colors as integers so that configurations are functions $\mathbb{Z}^d…
As Python is increasingly being adopted for large and complex programs, the importance of static analysis for Python (such as type inference) grows. Unfortunately, static analysis for Python remains a challenging task due to its dynamic…