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Making a linguistic theory is like making a programming language: one typically devises a type system to delineate the acceptable utterances and a denotational semantics to explain observations on their behavior. Via this connection, the…
We consider fragments of first-order logic and as models we allow finite and infinite words simultaneously. The only binary relations apart from equality are order comparison < and the successor predicate +1. We give characterizations of…
Autonomous systems embedded with machine learning modules often rely on deep neural networks for classifying different objects of interest in the environment or different actions or strategies to take for the system. Due to the…
We study the complexity of basic regular operations on languages represented by incomplete deterministic or nondeterministic automata, in which all states are final. Such languages are known to be prefix-closed. We get tight bounds on both…
Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology-Based Query Answering. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure…
We study decidability of verification problems for timed automata extended with unbounded discrete data structures. More detailed, we extend timed automata with a pushdown stack. In this way, we obtain a strong model that may for instance…
A logic satisfies the interpolation property provided that whenever a formula {\Delta} is a consequence of another formula {\Gamma}, then this is witnessed by a formula {\Theta} which only refers to the language common to {\Gamma} and…
We consider the verification of omega-regular linear temporal properties of concurrent programs running under weak memory semantics. We observe that in particular, these properties may enforce liveness clauses, whose verification in this…
Let $X=(V\!X,E\!X)$ be an infinite, locally finite, connected graph without loops or multiple edges. We consider the edges to be oriented, and $E\!X$ is equipped with an involution which inverts the orientation. Each oriented edge is…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Modal logics are widely used in computer science. The complexity of their satisfiability problems has been an active field of research since the 1970s. We prove that even very "simple" modal logics can be undecidable: We show that there is…
The notion of delays arises naturally in many computational models, such as, in the design of circuits, control systems, and dataflow languages. In this work, we introduce \emph{automata with delay blocks} (ADBs), extending finite state…
Minimizing the size of finite automata is a fundamental problem in theoretical computer science. Beyond standard minimization, further reductions can be achieved by decomposing an automaton into smaller components whose languages combine…
We prove that the positive fragment of first-order intuitionistic logic in the language with two variables and a single monadic predicate letter, without constants and equality, is undecidable. This holds true regardless of whether we…
A tower between two regular languages is a sequence of strings such that all strings on odd positions belong to one of the languages, all strings on even positions belong to the other language, and each string can be embedded into the next…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…
We study the task, for a given language $L$, of enumerating the (generally infinite) sequence of its words, without repetitions, while bounding the delay between two consecutive words. To allow for delay bounds that do not depend on the…
We present new results on finite satisfiability of logics with counting and arithmetic. One result is a tight bound on the complexity of satisfiability of logics with so-called local Presburger quantifiers, which sum over neighbors of a…
A data word is a sequence of pairs of a letter from a finite alphabet and an element from an infinite set, where the latter can only be compared for equality. Safety one-way alternating automata with one register on infinite data words are…