Relating Weight Constraint and Aggregate Programs: Semantics and Representation

Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint programs and the answer set semantics based on conditional satisfaction for aggregate programs. Both classes of programs are instances of logic programs with constraints, and in particular, the answer set semantics for aggregate programs can be applied to weight constraint programs. We show that the two semantics are closely related. First, we show that for a broad class of weight constraint programs, called strongly satisfiable programs, the two semantics coincide. When they disagree, a stable model admitted by the stable model semantics may be circularly justified. We show that the gap between the two semantics can be closed by transforming a weight constraint program to a strongly satisfiable one, so that no circular models may be generated under the current implementation of the stable model semantics. We further demonstrate the close relationship between the two semantics by formulating a transformation from weight constraint programs to logic programs with nested expressions which preserves the answer set semantics. Our study on the semantics leads to an investigation of a methodological issue, namely the possibility of compact representation of aggregate programs by weight constraint programs. We show that almost all standard aggregates can be encoded by weight constraints compactly. This makes it possible to compute the answer sets of aggregate programs using the ASP solvers for weight constraint programs. This approach is compared experimentally with the ones where aggregates are handled more explicitly, which show that the weight constraint encoding of aggregates enables a competitive approach to answer set computation for aggregate programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP), 2011. 30 page

Tight Logic Programs

This note is about the relationship between two theories of negation as failure -- one based on program completion, the other based on stable models, or answer sets. Francois Fages showed that if a logic program satisfies a certain syntactic condition, which is now called ``tightness,'' then its stable models can be characterized as the models of its completion. We extend the definition of tightness and Fages' theorem to programs with nested expressions in the bodies of rules, and study tight logic programs containing the definition of the transitive closure of a predicate.Comment: To appear in Special Issue of the Theory and Practice of Logic Programming Journal on Answer Set Programming, 200

Combining Static and Dynamic Analysis for Vulnerability Detection

In this paper, we present a hybrid approach for buffer overflow detection in C code. The approach makes use of static and dynamic analysis of the application under investigation. The static part consists in calculating taint dependency sequences (TDS) between user controlled inputs and vulnerable statements. This process is akin to program slice of interest to calculate tainted data- and control-flow path which exhibits the dependence between tainted program inputs and vulnerable statements in the code. The dynamic part consists of executing the program along TDSs to trigger the vulnerability by generating suitable inputs. We use genetic algorithm to generate inputs. We propose a fitness function that approximates the program behavior (control flow) based on the frequencies of the statements along TDSs. This runtime aspect makes the approach faster and accurate. We provide experimental results on the Verisec benchmark to validate our approach.Comment: There are 15 pages with 1 figur

The preliminary SOL (Sizing and Optimization Language) reference manual

The Sizing and Optimization Language, SOL, a high-level special-purpose computer language has been developed to expedite application of numerical optimization to design problems and to make the process less error-prone. This document is a reference manual for those wishing to write SOL programs. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler and runtime library routines. An overview of SOL appears in NASA TM 100565