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Sequential hypothesis testing asks for decision rules that update as data arrive. A natural goal is \emph{eventual correctness}: the rule may change its mind early on, but it should make only finitely many wrong decisions almost surely.…
Multi-stack pushdown systems are a well-studied model of concurrent computation using threads with first-order procedure calls. While, in general, reachability is undecidable, there are numerous restrictions on stack behaviour that lead to…
What do applications like semantic optimization, data exchange and integration, answering queries under dependencies, query reformulation with constraints, and data cleaning have in common? All these applications can be processed by the…
The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded…
We solve a well known and long-standing open problem in database theory, proving that Conjunctive Query Finite Determinacy Problem is undecidable. The technique we use builds on the top of our Red Spider method which we developed in our…
Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep…
Motivated by the success of bounded model checking framework for finite state machines, Ouaknine and Worrell proposed a time-bounded theory of real-time verification by claiming that restriction to bounded-time recovers decidability for…
For a given set of queries (which are expressions in some query language) $\mathcal{Q}=\{Q_1$, $Q_2, \ldots Q_k\}$ and for another query $Q_0$ we say that $\mathcal{Q}$ determines $Q_0$ if -- informally speaking -- for every database…
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…
Infinite games with imperfect information are known to be undecidable unless the information flow is severely restricted. One fundamental decidable case occurs when there is a total ordering among players, such that each player has access…
While machine learning has advanced through massive parallelization, we identify a critical blind spot: some problems are fundamentally sequential. These "inherently serial" problems-from mathematical reasoning to physical simulations to…
Discovering interpretable patterns for classification of sequential data is of key importance for a variety of fields, ranging from genomics to fraud detection or more generally interpretable decision-making. In this paper, we propose a…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
Termination of logic programs depends critically on the selection rule, i.e. the rule that determines which atom is selected in each resolution step. In this article, we classify programs (and queries) according to the selection rules for…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
We study reasoning with existential rules to perform query answering over streams of data. On static databases, this problem has been widely studied, but its extension to rapidly changing data has not yet been considered. To bridge this…
Contrary to the sequential world, the processes involved in a distributed system do not necessarily know when a computation is globally finished. This paper investigates the problem of the detection of the termination of local computations.…
Declarative Distributed Systems (DDSs) are distributed systems grounded in logic programming. Although DDS model-checking is undecidable in general, we detect decidable cases by tweaking the data-source bounds, the message expressiveness,…
Multi-label classification (MLC) is a supervised learning problem in which, contrary to standard multiclass classification, an instance can be associated with several class labels simultaneously. In this chapter, we advocate a rule-based…