We present a determinization construction for weighted tree automata using factorizations. Among others, this result subsumes a previous result for determinization of weighted string automata using factorizations (Kirsten and Mäurer, 2005) and two previous results for weighted tree automata, one of them not using factorizations (Borchardt, 2004) and one of them restricted to nonrecursive automa...

We introduce the notion of operational resolution, i.e., an isotone map from a powerset to a poset that meets two additional conditions, which generalizes the description of states as the atoms in a property lattice (Piron, 1976 and Aerts, 1982) or as the underlying set of a closure operator (Aerts, 1994 and Moore, 1995). We study the structure preservance of the related state transitions and s...

The category Rel(Set) of sets and relations can be described as a category of spans and as the Kleisli category for the powerset monad. A set-functor can be lifted to a functor on Rel(Set) iff it preserves weak pullbacks. We show that these results extend to the enriched setting, if we replace sets by posets or preorders. Preservation of weak pullbacks becomes preservation of exact lax squares....

The one purpose of this little Note is to show that formal arguments need not be lengthy at all; on the contrary, they are often the most compact rendering of the argument. Its other purpose is to show the strong heuristic guidance that is available to us when we design such calculational proofs in sufficiently small, explicit steps. We illustrate our approach on Georg Cantor’s classic diagonal...

A minimal permutation representation of a finite group G is a faithful G-set with the smallest possible cardinality. We study the structure of such representations and show that for most groups they may be obtained by a greedy construction. It follows that whenever the algorithm works (except when central involutions intervene) all minimal permutation representations have the same set of orbit ...

We extend the Kripke-like model theory given in 10] for a fragment of rst-order hereditary Harrop formulae to include negated atoms in goals. This gives us a formal framework in which to study the role of Negation as Failure rule. The class of predicates for which Negation As Failure is applicable is discussed, as well as the predicates for which some other form of negation will need to be used...

A fast, scalable and memory-efficient method for static decoding graph construction is presented. As an alternative to the traditional transducer-based approach, it is based on incremental composition. Memory efficiency is achieved by combining composition, determinization and minimization into a single step, thus eliminating large intermediate graphs. We have previously reported the use of inc...

Many loops in probabilistic inference map almost every individual in their domain to the same result. Running such loops symbolically takes time sublinear in the domain size. Using normalization by evaluation with first-class delimited continuations, we lift inference procedures to reap this speed-up without interpretive overhead. To express nested loops, we use multiple control delimiters for ...

This paper investigates aspects of measure and randomness in the context of locale theory (point-free topology). We prove that every measure (σ-continuous valuation) μ, on the σ-frame of opens of a fitted σ-locale X, extends to a measure on the lattice of all σ-sublocales of X (Theorem 1). Furthermore, when μ is a finite measure with μ(X) = M , the σ-locale X has a smallest σ-sublocale of measu...