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...

In this paper, we study the structure of underlying automata based constructions for solving the LTL realizability problem. We show how to reduce the LTL realizability problem to a game with an observer which checks that the game visits a bounded number of times accepting states of a universal co-Büchi word automaton. We show that such an observer can be made deterministic and that this determi...

When two nominal constituents are in a relation of dependency in the Bantu languages, the syntactically dependent constituent is usually introduced by a relator. In Bantu studies this relator is called connective (also associative, genitive or connexive) element (or pronoun, clitic, prefix, marker or particle). The order is HEAD (R1) RELATOR (REL) DEPENDENT (R2). R1 and R2 are short for first a...