It is known that implications in powerset-based closure systems correspond to Horn approximations in propositional logic frameworks. Here we focus on the problem of implications between injective partial orders. We set up the definitions that allow one to apply standard constructions of implications, and formally characterize the propositional theory obtained. We describe also some experimental...

Church’s Problem, stated fifty years ago, asks for a finitestate machine that realizes the transformation of an infinite sequence α into an infinite sequence β such that a requirement on (α, β), expressed in monadic second-order logic, is satisfied. We explain how three fundamental techniques of automata theory play together in a solution of Church’s Problem: Determinization (starting from the ...

The inversion method proposed by Glück and Kawabe uses grammar programs as intermediate results that comprise sequences of operations (data generation, matching, etc.). The determinization method used in the inversion method fails for a grammar program of which the collection of item sets causes a conflict even if there exists a deterministic program equivalent to the grammar program. In this p...

We present and analyse an approach to image reconstruction problems with imperfect forward models based on partially ordered spaces – Banach lattices. In this approach, errors in the data and in the forward models are described using order intervals. The method can be characterised as the lattice analogue of the residual method, where the feasible set is defined by linear inequality constraints...

A principle is proposed that organizes verbs in the lexicon according to their meaning and the number of arguments they require. This principle, which we call the Paradigmatic Structure, acts as a filter for the permanent lexicon, letting all verb stems into the lexicon but only some morphological derivatives. The effects of the Paradigmatic Structure are observed in blocking, in which some but...

The stochastic shortest path problem (SSP) is a highly expressive model for probabilistic planning. The computational hardness of SSPs has sparked interest in determinization-based planners that can quickly solve large problems. However, existing methods employ a simplistic approach to determinization. In particular, they ignore the possibility of tailoring the determinization to the specific c...

The two determinization procedures of Safra and MullerSchupp for Büchi automata are compared, based on an implementation in a program called OmegaDet.

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kinetic equations with positive collision operators Abstract We consider " forward-backward " parabolic equations in the abstract form Jdψ/dx+Lψ = 0, 0 < x < τ ≤ ∞, where J and L are operators in a Hilbert space H such that J = J * = J −1 , L = L * ≥ 0, and ker L = 0. The following theorem is proved: if the operator B = JL is similar to a self-adjoint operator, then associated half-range bounda...