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In this paper we consider a number of natural decision problems involving k-regular sequences. Specifically, they arise from - lower and upper bounds on growth rate; in particular boundedness, - images, - regularity (recognizability by a…
We investigate the decidability of the emptiness problem for three classes of distributed automata. These devices operate on finite directed graphs, acting as networks of identical finite-state machines that communicate in an infinite…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires…
In various models of one-way pushdown automata, the explicit use of two designated endmarkers on a read-once input tape has proven to be extremely useful for making a conscious, final decision on the acceptance/rejection of each input word…
Deadlock detection in recursive programs that admit dynamic resource creation is extremely complex and solutions either give imprecise answers or do not scale. We define an algorithm for detecting deadlocks of "linear recursive programs" of…
We introduce and study the repetitive variants of the deterministic and the nondeterministic finite automaton with translucent words (DFAwtw and NFAwtw). On seeing the right sentinel, a repetitive NFAwtw need not halt immediately, accepting…
Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called "iterated…
For a given regular language of infinite trees, one can ask about the minimal number of priorities needed to recognize this language with a non-deterministic, alternating, or weak alternating parity automaton. These questions are known as,…
Many different deletion operations are investigated applied to languages accepted by one-way and two-way deterministic reversal-bounded multicounter machines, deterministic pushdown automata, and finite automata. Operations studied include…
The paper considers algorithmic properties of classical and non-classical first-order logics and theories in bounded languages. The main idea is to prove the undecidability of various fragments of classical and non-classical first-order…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Length constraints restrict valid substitutions of…
In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. These definitions are stated unambiguously through executable…
Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…
In a recent article, we introduced and studied a precise class of dynamical systems called solvable systems. These systems present a dynamic ruled by discontinuous ordinary differential equations with solvable right-hand terms and unique…
We show that the equivalence of deterministic linear top-down tree-to-word transducers is decidable in polynomial time. Linear tree-to-word transducers are non-copying but not necessarily order-preserving and can be used to express XML and…
Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable.…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
Open Answer Set Programming (OASP) is an attractive framework for integrating ontologies and rules. In general OASP is undecidable. In previous work we provided a tableau-based algorithm for satisfiability checking w.r.t. forest logic…