ConSUS: A light-weight program conditioner

Program conditioning consists of identifying and removing a set of statements which cannot be executed when a condition of interest holds at some point in a program. It has been applied to problems in maintenance, testing, re-use and re-engineering. All current approaches to program conditioning rely upon both symbolic execution and reasoning about symbolic predicates. The reasoning can be performed by a ‘heavy duty’ theorem prover but this may impose unrealistic performance constraints. This paper reports on a lightweight approach to theorem proving using the FermaT Simplify decision procedure. This is used as a component to ConSUS, a program conditioning system for the Wide Spectrum Language WSL. The paper describes the symbolic execution algorithm used by ConSUS, which prunes as it conditions. The paper also provides empirical evidence that conditioning produces a significant reduction in program size and, although exponential in the worst case, the conditioning system has low degree polynomial behaviour in many cases, thereby making it scalable to unit level applications of program conditioning

Shapes of topological RNA structures

A topological RNA structure is derived from a diagram and its shape is obtained by collapsing the stacks of the structure into single arcs and by removing any arcs of length one. Shapes contain key topological, information and for fixed topological genus there exist only finitely many such shapes. We shall express topological RNA structures as unicellular maps, i.e. graphs together with a cyclic ordering of their half-edges. In this paper we prove a bijection of shapes of topological RNA structures. We furthermore derive a linear time algorithm generating shapes of fixed topological genus. We derive explicit expressions for the coefficients of the generating polynomial of these shapes and the generating function of RNA structures of genus $g$. Furthermore we outline how shapes can be used in order to extract essential information of RNA structure databases.Comment: 27 pages, 11 figures, 2 tables. arXiv admin note: text overlap with arXiv:1304.739

Closing the Gap for Pseudo-Polynomial Strip Packing

Two-dimensional packing problems are a fundamental class of optimization problems and Strip Packing is one of the most natural and famous among them. Indeed it can be defined in just one sentence: Given a set of rectangular axis parallel items and a strip with bounded width and infinite height, the objective is to find a packing of the items into the strip minimizing the packing height. We speak of pseudo-polynomial Strip Packing if we consider algorithms with pseudo-polynomial running time with respect to the width of the strip. It is known that there is no pseudo-polynomial time algorithm for Strip Packing with a ratio better than 5/4 unless P = NP. The best algorithm so far has a ratio of 4/3 + epsilon. In this paper, we close the gap between inapproximability result and currently known algorithms by presenting an algorithm with approximation ratio 5/4 + epsilon. The algorithm relies on a new structural result which is the main accomplishment of this paper. It states that each optimal solution can be transformed with bounded loss in the objective such that it has one of a polynomial number of different forms thus making the problem tractable by standard techniques, i.e., dynamic programming. To show the conceptual strength of the approach, we extend our result to other problems as well, e.g., Strip Packing with 90 degree rotations and Contiguous Moldable Task Scheduling, and present algorithms with approximation ratio 5/4 + epsilon for these problems as well