Related papers: First-order definable string transformations
Within the model-theoretic framework for supervised learning introduced by Grohe and Tur\'an (TOCS 2004), we study the parameterized complexity of learning concepts definable in monadic second-order logic (MSO). We show that the problem of…
A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be…
We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
Permutations can be viewed as pairs of linear orders, or more formally as models over a signature consisting of two binary relation symbols. This approach was adopted by Albert, Bouvel and F\'eray, who studied the expressibility of…
We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present…
Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In…
Automated reasoning is critical in domains such as law and governance, where verifying claims against facts in documents requires both accuracy and interpretability. Recent work adopts structured reasoning pipelines that translate natural…
This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…
We show that the existence of a first-order formula separating two monadic second order formulas over countable ordinal words is decidable. This extends the work of Henckell and Almeida on finite words, and of Place and Zeitoun on…
We present a new model of computation, described in terms of monoidal categories. It conforms the Church-Turing Thesis, and captures the same computable functions as the standard models. It provides a succinct categorical interface to most…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
We consider the class of languages defined in the 2-variable fragment of the first-order logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier…
We study the sequence-to-sequence mapping capacity of transformers by relating them to finite transducers, and find that they can express surprisingly large classes of transductions. We do so using variants of RASP, a programming language…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…
FO transductions, aperiodic deterministic two-way transducers, as well as aperiodic streaming string transducers are all equivalent models for first order definable functions. In this paper, we solve the long standing open problem of…
Tasks that model the relation between pairs of tokens in a string are a vital part of understanding natural language. Such tasks, in general, require exhaustive pair-wise comparisons of tokens, thus having a quadratic runtime complexity in…
Temporal logics are widely used by the Formal Methods and AI communities. Linear Temporal Logic is a popular temporal logic and is valued for its ease of use as well as its balance between expressiveness and complexity. LTL is equivalent in…
A transducer is finite-valued if for some bound k, it maps any given input to at most k outputs. For classical, one-way transducers, it is known since the 80s that finite valuedness entails decidability of the equivalence problem. This…
We investigate families of infinite automata for context-sensitive languages. An infinite automaton is an infinite labeled graph with two sets of initial and final vertices. Its language is the set of all words labelling a path from an…