The most efficient algorithms for several network problems like minimum cost flow and the maximum weight matching problem follow the primal-dual paradigm. These algorithms perform arithmetic (additions and subtractions) on numbers of magnitude O(nC) when the edge weights (also called costs) are integers bounded by C and n denotes the number of vertices. Under the standard assumption that arithm...

We present the design and implementation of an exact rational arithmetic package for the programming language Caml, an ML dialect close to the original LCF-ML. Our arithmetic, written almost entirely in Caml, combines eeciency, power and exibility. For eeciency reasons, the package provides several diier-ent basic types to represent numbers, and to reinforce exibility, it implements many functi...

This paper presents certain important aspects of the fuzzy logic extension, one of which is OFN. It includes basic definitions of that discipline. It also compares fuzzy logic arithmetic with the arithmetic of ordered fuzzy numbers in L-R notation. Computational experiments were based on fuzzy observation of the impounding basin. The results of the study show that there is a connection between ...

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgements of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to s...

Interactive proofs are de ned in terms of a conversation between two Turing machines, the prover and the veri er. We de ne an equivalent kind of proof in terms more usual for logic: our proofs are derivations from axioms by rules of inference. Namely, we consider proofs in formal arithmetic extended by some additional rule that uses random numbers. Such a proof can be considerably shorter than ...

In this paper a new aggregation operator for a class of LR Fuzzy Numbers i.e., Triangular Fuzzy Numbers (TFNs) in which the Land Rapex angles of the piecewise continuous linear membership function of the composite or resultant or aggregate TFN are the arithmetic means of the corresponding Land Rapex angles of the individual TFNs is proposed. The Land Rapex angles have been treated independently...