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We present a type system that combines, in a controlled way, first-order polymorphism with intersectiontypes, union types, and subtyping, and prove its safety. We then define a type reconstruction algorithm that issound and terminating.…
The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related lambda calculi and some from the…
This paper presents a new solution to the containment problem for extended regular expressions that extends basic regular expressions with intersection and complement operators and consider regular expressions on infinite alphabets based on…
This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…
The scope of this work is the constraint-based synthesis of termination arguments for the restricted class of programs called linear lasso programs. A termination argument consists of a ranking function as well as a set of supporting…
We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the…
Lexically constrained machine translation allows the user to manipulate the output sentence by enforcing the presence or absence of certain words and phrases. Although current approaches can enforce terms to appear in the translation, they…
Reduction of combinatorial filters involves compressing state representations that robots use. Such optimization arises in automating the construction of minimalist robots. But exact combinatorial filter reduction is an NP-complete problem…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
This paper continues a systematic and comprehensive study on the structural properties of CFL functions, which are in general multi-valued partial functions computed by one-way one-head nondeterministic pushdown automata equipped with…
The recently introduced dependent typed higher-order logic (DHOL) offers an interesting compromise between expressiveness and automation support. It sacrifices the decidability of its type system in order to significantly extend its…
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…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Recent work has shown that large pretrained Language Models (LMs) can not only perform remarkably well on a range of Natural Language Processing (NLP) tasks but also start improving on reasoning tasks such as arithmetic induction, symbolic…
We investigate the possibility of modelling the syntax and semantics of natural language by constraints, or rules, imposed by the multi-dimensional type theory Nabla. The only multiplicity we explicitly consider is two, namely one dimension…
The theory of higher-dimensional automata (HDAs) has seen rapid progress in recent years, and first applications, notably to Petri net analysis, are starting to show. It has, however, emerged that HDAs themselves often are too strict a…
Li and Pedrycz [Y. M. Li, W. Pedrycz, Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids, Fuzzy Sets and Systems 156 (2005) 68--92] have proved fundamental results that provide different…
We prove lower bounds on the length of regular expressions for finite languages by methods from arithmetic circuit complexity. First, we show a reduction: the length of a regular expression for a language $L\subseteq \{0,1\}^n$ is bounded…
Finite automata are used to encode geometric figures, functions and can be used for image compression and processing. The original approach is to represent each point of a figure in $\mathbb{R}^n$ as a convolution of its $n$ coordinates…
This paper studies balance properties for billiard words. Billiard words generalize Sturmian words by coding trajectories in hypercubic billiards. In the setting of aperiodic order, they also provide the simplest examples of quasicrystals,…