Related papers: Decidability and k-Regular Sequences
Techniques for decision making with knowledge of linear constraints on condition probabilities are examined. These constraints arise naturally in many situations: upper and lower condition probabilities are known; an ordering among the…
We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula phi(X,x) that is positive in X, it is decidable whether the…
Systems of decision rules and decision trees are widely used as a means for knowledge representation, as classifiers, and as algorithms. They are among the most interpretable models for classifying and representing knowledge. The study of…
In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider…
We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, B\"uchi, coB\"uchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and…
We study a class of two-stage stochastic programs in which the second stage includes a set of components with uncertain capacity, and the expression for the distribution function of the uncertain capacity includes first-stage variables.…
Decidability of the determinization problem for weighted automata over the semiring $(\mathbb{Z} \cup {-\infty}, \max, +)$, WA for short, is a long-standing open question. We propose two ways of approaching it by constraining the search…
In our paper [G{\l}uch, Marcinkowski, Ostropolski-Nalewaja, LICS ACM, 2018] we have solved an old problem stated in [Calvanese, De Giacomo, Lenzerini, Vardi, SPDS ACM, 2000] showing that query determinacy is undecidable for Regular Path…
Finite-state tree automata are a well studied formalism for representing term languages. This paper studies the problem of determining the regularity of the set of instances of a finite set of terms with variables, where each variable is…
Given a sequence of independent random variables with a common continuous distribution, we consider the online decision problem where one seeks to minimize the expected value of the time that is needed to complete the selection of a…
We are lifting classical problems from single instances to regular sets of instances. The task of finding a positive instance of the combinatorial problem $P$ in a potentially infinite given regular set is equivalent to the so called…
We study a class of elliptic problems, involving a $k$-Hessian and a very fast-growing nonlinearity, on a unit ball. We prove the existence of a radial singular solution and obtain its exact asymptotic behavior in a neighborhood of the…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
We study the model-checking problem for recursion schemes: does the tree generated by a given higher-order recursion scheme satisfy a given logical sentence. The problem is known to be decidable for sentences of the MSO logic. We prove…
Deep learning models have been the subject of study from various perspectives, for example, their training process, interpretation, generalization error, robustness to adversarial attacks, etc. A trained model is defined by its decision…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
The following problem is shown undecidable: given regular languages L,K of finite trees, decide if there exists a deterministic tree-walking automaton which accepts all trees in L and rejects all trees in K. The proof uses a technique of…
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…
It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections…
The knapsack problem is a classic optimisation problem that has been recently extended in the setting of groups. Its study reveals to be interesting since it provides many different behaviours, depending on the considered class of groups.…