An Overview of Backtrack Search Satisfiability Algorithms

Propositional Satisfiability (SAT) is often used as the underlying model for a significan

On Different Strategies for Eliminating Redundant Actions from Plans

Satisficing planning engines are often able to generate plans in a reasonable time, however, plans are often far from optimal. Such plans often contain a high number of redundant actions, that are actions, which can be removed without affecting the validity of the plans. Existing approaches for determining and eliminating redundant actions work in polynomial time, however, do not guarantee eliminating the "best" set of redundant actions, since such a problem is NP-complete. We introduce an approach which encodes the problem of determining the "best" set of redundant actions (i.e. having the maximum total-cost) as a weighted MaxSAT problem. Moreover, we adapt the existing polynomial technique which greedily tries to eliminate an action and its dependants from the plan in order to eliminate more expensive redundant actions. The proposed approaches are empirically compared to existing approaches on plans generated by state-of-the-art planning engines on standard planning benchmark

An Atypical Survey of Typical-Case Heuristic Algorithms

Heuristic approaches often do so well that they seem to pretty much always give the right answer. How close can heuristic algorithms get to always giving the right answer, without inducing seismic complexity-theoretic consequences? This article first discusses how a series of results by Berman, Buhrman, Hartmanis, Homer, Longpr\'{e}, Ogiwara, Sch\"{o}ening, and Watanabe, from the early 1970s through the early 1990s, explicitly or implicitly limited how well heuristic algorithms can do on NP-hard problems. In particular, many desirable levels of heuristic success cannot be obtained unless severe, highly unlikely complexity class collapses occur. Second, we survey work initiated by Goldreich and Wigderson, who showed how under plausible assumptions deterministic heuristics for randomized computation can achieve a very high frequency of correctness. Finally, we consider formal ways in which theory can help explain the effectiveness of heuristics that solve NP-hard problems in practice.Comment: This article is currently scheduled to appear in the December 2012 issue of SIGACT New

Optimization Modulo Theories with Linear Rational Costs

In the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories of practical interest (e.g., linear arithmetic, arrays, bit-vectors). Surprisingly, little work has been done to extend SMT to deal with optimization problems; in particular, we are not aware of any previous work on SMT solvers able to produce solutions which minimize cost functions over arithmetical variables. This is unfortunate, since some problems of interest require this functionality. In the work described in this paper we start filling this gap. We present and discuss two general procedures for leveraging SMT to handle the minimization of linear rational cost functions, combining SMT with standard minimization techniques. We have implemented the procedures within the MathSAT SMT solver. Due to the absence of competitors in the AR, FV and SMT domains, we have experimentally evaluated our implementation against state-of-the-art tools for the domain of linear generalized disjunctive programming (LGDP), which is closest in spirit to our domain, on sets of problems which have been previously proposed as benchmarks for the latter tools. The results show that our tool is very competitive with, and often outperforms, these tools on these problems, clearly demonstrating the potential of the approach.Comment: Submitted on january 2014 to ACM Transactions on Computational Logic, currently under revision. arXiv admin note: text overlap with arXiv:1202.140