Related papers: First-order definable string transformations
Sequential Constraint Grammar (SCG) (Karlsson, 1990) and its extensions have lacked clear connections to formal language theory. The purpose of this article is to lay a foundation for these connections by simplifying the definition of…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
We study the first-order model checking problem on two generalisations of pushdown graphs. The first class is the class of nested pushdown trees. The other is the class of collapsible pushdown graphs. Our main results are the following.…
Skolem functions play a central role in the study of first order logic, both from theoretical and practical perspectives. While every Skolemized formula in first-order logic makes use of Skolem constants and/or functions, not all such…
We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way---for example, the set of all word pairs u,v where v is a prefix of u independently of what the alphabet is. Current…
In this paper we describe an approach to constraint-based syntactic theories in terms of finite tree automata. The solutions to constraints expressed in weak monadic second order (MSO) logic are represented by tree automata recognizing the…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
Motivated by a recent conjecture concerning the expressiveness of declarative networking, we propose a formal computation model for "eventually consistent" distributed querying, based on relational transducers. A tight link has been…
We give a new simple proof of the decidability of the First Order Theory of (omega^omega^i,+) and the Monadic Second Order Theory of (omega^i,<), improving the complexity in both cases. Our algorithm is based on tree automata and a new…
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
Motivated by real-time monitoring and data processing applications, we develop a formal theory of quantitative queries for streaming data that can be evaluated efficiently. We consider the model of unambiguous Cost Register Automata (CRAs),…
Phase transitions mark qualitative reorganizations of collective behavior, yet identifying their boundaries remains challenging whenever analytic solutions are absent and conventional simulations fail. Here we introduce learnability as a…
Intelligent voice assistants, such as Apple Siri and Amazon Alexa, are widely used nowadays. These task-oriented dialogue systems require a semantic parsing module in order to process user utterances and understand the action to be…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
Many common sequential data sources, such as source code and natural language, have a natural tree-structured representation. These trees can be generated by fitting a sequence to a grammar, yielding a hierarchical ordering of the tokens in…
A classic result in formal language theory is the equivalence among non-counting, or aperiodic, regular languages, and languages defined through star-free regular expressions, or first-order logic. Past attempts to extend this result beyond…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
The volume and diversity of digital information have led to a growing reliance on Machine Learning techniques, such as Natural Language Processing, for interpreting and accessing appropriate data. While vector and graph embeddings represent…
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
Analogical reasoning is a hallmark of human intelligence, enabling us to solve new problems by transferring knowledge from one situation to another. Yet, developing artificial intelligence systems capable of robust human-like analogical…