We study the space complexity of the cutting planes proof system, in which the lines in a proof are integral linear inequalities. We measure the space used by a refutation as the number of linear inequalities that need to be kept on a blackboard while verifying it. We show that any unsatisfiable set of linear inequalities has a cutting planes refutation in space five. This is in contrast to the...

Recently, Blum and Micali (1982) described a pseudorandum number generator that transforms m-bit seeds to ink-bit pseudorandom numbers, for any integer k. Under the assumption that the discrete logarithm problem cannot be solved by polynomial-size combinational logic circuits, they show that the pseudorandom numbers generated are good in the sense that no polynomial-size circuit can determine t...

In Air Traffic Control (ATC), controller workload has been an important topic of research. Many studies have been conducted in the past to uncover the art of evaluating workload. Many of which have been centered on the sector complexity or task demand based studies [1,2,3,4]. Moreover, all have the aim to understand the workload that was imposed on the controller and the extent to which the wor...

It is known that any two triangulations of a compact 3–manifold are related by finite sequences of certain local transformations. We prove here an upper bound for the length of a shortest transformation sequence relating any two triangulations of the 3–dimensional projective space, in terms of the number of tetrahedra. MSC–class: 57Q25; 57Q15.

Performance and complexity are considered here as two orthogonal axes. Performance metrics are recalled. Then different complexity metrics and scales are proposed. Different definitions of complexity are used depending on the considered level of abstraction. Finally, SOI and bulk CMOS technologies are compared in this space.

During the last decade, an active line of research in proof complexity has been to study space complexity and timespace trade-offs for proofs. Besides being a natural complexity measure of intrinsic interest, space is also an important issue in SAT solving. For the polynomial calculus proof system, the only previously known space lower bound is for CNF formulas of unbounded width in [Alekhnovic...

Driven by the rising popularity of cloud storage, the costs associated with implementing reliable storage services from a collection of fault-prone servers have recently become an actively studied question. The well-known ABD result shows that an f -tolerant register can be emulated using a collection of 2f + 1 fault-prone servers each storing a single read-modify-write object, which is known t...