Related papers: Efficient Analysis of Unambiguous Automata Using M…
We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…
In the present paper I formulate a framework that accommodates many unambiguous discrimination problems. I show that the prior information about any type of constituent (state, channel, or observable) allows us to reformulate the…
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo…
In this paper we present a mathematical formulation for the omega invariant of a numerical semigroup for each of its minimal generators. The model consists of solving a problem of optimizing a linear function over the efficient set of a…
We introduce a method for translating an alternating weak B\"uchi automaton (AWA), which corresponds to a Linear Dynamic Logic (LDL) formula, to an unambiguous B\"uchi automaton (UBA). Our translations generalise constructions for Linear…
Complementation of B\"uchi automata, required for checking automata containment, is of major theoretical and practical interest in formal verification. We consider two recent approaches to complementation. The first is the rank-based…
In this paper, we study the word problem for automaton semigroups and automaton groups from a complexity point of view. As an intermediate concept between automaton semigroups and automaton groups, we introduce automaton-inverse semigroups,…
Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…
We develop an algorithm that computes strongly continuous semigroups on infinite-dimensional Hilbert spaces with explicit error control. Given a generator $A$, a time $t>0$, an arbitrary initial vector $u_0$ and an error tolerance…
We introduce a new fragment of Linear temporal logic (LTL) called LIO and a new class of Buechi automata (BA) called Almost linear Buechi automata (ALBA). We provide effective translations between LIO and ALBA showing that the two…
We introduce first order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first order formulae, with states and internal variables given by uninterpreted…
We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a…
For the rational group algebra $\mathbb{Q}G$ of a finite group $G$, we provide an effective method to compute a complete set of matrix units and, in particular, primitive orthogonal idempotents in a simple component of $\mathbb{Q}G$, which…
Abu Radi and Kupferman (2019) demonstrated the efficient minimization of history-deterministic (transition-based) co-B\"uchi automata, building on the results of Kuperberg and Skrzypczak (2015). We give a congruence-based description of…
Automata over infinite words, also known as omega-automata, play a key role in the verification and synthesis of reactive systems. The spectrum of omega-automata is defined by two characteristics: the acceptance condition (e.g. B\"uchi or…
Increasing interest in integrating advanced robotics within manufacturing has spurred a renewed concentration in developing real-time scheduling solutions to coordinate human-robot collaboration in this environment. Traditionally, the…
We introduce the subsemigroup complex of a finite semigroup S as a (boolean representable) simplicial complex defined through chains in the lattice of subsemigroups of S. We present a research program for such complexes, illustrated through…
Notions of simulation, among other uses, provide a computationally tractable and sound (but not necessarily complete) proof method for language inclusion. They have been comprehensively studied by Lynch and Vaandrager for nondeterministic…
Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…
Spatial numerical integration is essential for finite element analysis. Currently, numerical integration schemes, mostly based on Gauss quadrature, are widely used. Herein, we present an alternative semi-analytical approach for mass matrix…