We present a seemingly new normal form for braids, where every braid is expressed using a word in a regular language on some simple alphabet of elementary braids. This normal form stems from analysing the geometric action of braid groups on curves in a punctured disk.

This research explores the problem of cooperation. It is possible to develop cooperative strategies for a specific environment, but those strategies are unlikely to apply to other environments. To avoid that problem, we work in an environment that is flexible enough to be used to describe an arbitrary environment. We have found a a method by which cooperation can be achieved in that environment...

We introduce a necessary and sufficient condition for the ω-extensionality rule of higherorder equational logic to be conservative over first-order many-sorted equational logic for ground first-order equations. This gives a precise condition under which computation in the higher-order initial model by term rewriting is possible. The condition is then generalised to characterise a normal form fo...

We present DepQBF 0.1, a new search-based solver for quantified boolean formulae (QBF). It integrates compact dependency graphs to overcome the restrictions imposed by linear quantifier prefixes of QBFs in prenex conjunctive normal form (PCNF). DepQBF 0.1 was placed first in the main track of QBFEVAL’10 in a score-based ranking. We provide a general system overview and describe selected orthogo...

We describe algorithmic methods for the Gauss-Manin connection of an isolated hypersurface singularity based on the microlocal structure of the Brieskorn lattice. They lead to algorithms for computing invariants like the monodromy, the spectrum, the spectral pairs, and M. Saito’s matrices A0 and A1. These algorithms use a normal form algorithm for the Brieskorn lattice, standard basis methods f...

In this paper we propose a Logic Calculator with three operation modes: evaluation of logical formulae; logical entailment and conversion of a formula to Disjunctive Normal Form (DNF) and Conjunctive Normal Form (CNF). It is worth noting there are no existing automated tools for these three computations integrated into one tool providing a graphical calculator format. Logic Calculator is availa...

We study homomorphisms of propositional formulas in CNF generalizing symmetries considered by Krishnamurthy. If φ : H → F is a homomorphism, then unsatisfiability of H implies unsatisfiability of F . Homomorphisms from F to a subset F ′ of F (endomorphisms) are of special interest, since in such case F and F ′ are satisfiability-equivalent. We show that smallest subsets F ′ of a formula F for w...

First-order Gödel logic with the projection operator △ (G∞) is an important many-valued as well as intermediate logic. In contrast to classical logic, the validity and the satisfiability problems of G∞ are not directly dual to each other. We nevertheless provide a uniform, computational treatment of both problems for prenex formulas by describing appropriate translations into sets of order clau...

In recent years, multi-agent epistemic planning has received attention from both dynamic logic and planning communities. Existing implementations of multi-agent epistemic planning are based on compilation into classical planning and suffer from various limitations, such as generating only linear plans, restriction to public actions, and incapability to handle disjunctive beliefs. In this paper,...

In learning from examples, the main goal is to use a collection of positive examples and a collection of negative examples to derive a Boolean expression which satisfies the requirements imposed by the examples. In order to represent such a Boolean expression, the conjunctive normal form (CNF) and the disjunctive normal form (DNF) have been proposed. This paper makes two contributions. First it...