The objective of this survey is to present the ideal theory of monoids, the so-called Green’s relations, and to illustrate the usefulness of this tool for solving automata related questions. We use Green’s relations for proving four classical results related to automata theory: The result of Schützenberger characterizing star-free languages, the theorem of factorization forests of Simon, the ch...

This paper presents an overview of algorithms for constructing automata from linear arithmetic constraints. It identifies one case in which the special structure of the automata that are constructed allows a linear-time determinization procedure to be used. Furthermore, it shows through theoretical analysis and experiments that the special structure of the constructed automata does, in quite a ...

We lay down the foundations for a pointfree theory of Pervin spaces. A space is set equipped with bounded sublattice its powerset, and it known that these objects characterize those quasi-uniform spaces are transitive totally bounded. The notion space, which we call Frith frame, consists frame generating sublattice. In this paper introduce study category frames show classical dual adjunction be...

In concurrency theory, various semantic equivalences on labelled transition systems are based on traces enriched or decorated with some additional observations. They are generally referred to as decorated traces, and examples include ready, failure, trace and complete trace equivalence. Using the generalized powerset construction, recently introduced by a subset of the authors [13], we give a c...

An often mentioned obstacle for the use of Dempster-Shafer theory for the handling of uncertainty in expert systems is the computational complexity of the theory. One cause of this complexity is the fact that in Dempster-Shafer theory the evidence is represented by a belief function which is induced by a basic probability assignment, i.e. a probability measure on the powerset of possible answer...

In multi-label learning, each instance in the training set is associated with a set of labels, and the task is to output a label set for each unseen instance. This paper describes a new method for multi-label classification based on the Dempster-Shafer theory of belief functions to classify an unseen instance on the basis of its k nearest neighbors. The proposed method generalizes an existing s...

Counterexample-based Refinement for Powerset Domains R. Manevich, J. Field , T. A. Henzinger, G. Ramalingam, and M. Sagiv 1 Tel Aviv University, {rumster,msagiv}@tau.ac.il 2 IBM T.J. Watson Research Center, [email protected] 3 EPFL, [email protected] 4 Microsoft Research India, [email protected] Abstract. Counterexample-guided abstraction refinement (CEGAR) is a powerful technique to scale auto...

Paredaens and Van Gucht proved that the at relational algebra has the same expressive power as the nested relational algebra, as far as queries over at relations and with at results are concerned. We provide a new, very direct proof of this fact using a simulation technique. Our technique is also applied to partially answer a question posed by Suciu and Paredaens regarding the complexity of eva...

We introduce the equational notion of a monadic bounded algebra (MBA), intended to capture algebraic properties of bounded quantification. The variety of all MBA’s is shown to be generated by certain algebras of two-valued propositional functions that correspond to models of monadic free logic with an existence predicate. Every MBA is a subdirect product of such functional algebras, a fact that...