30,248 research outputs found
A Logical Approach to Efficient Max-SAT solving
Weighted Max-SAT is the optimization version of SAT and many important
problems can be naturally encoded as such. Solving weighted Max-SAT is an
important problem from both a theoretical and a practical point of view. In
recent years, there has been considerable interest in finding efficient solving
techniques. Most of this work focus on the computation of good quality lower
bounds to be used within a branch and bound DPLL-like algorithm. Most often,
these lower bounds are described in a procedural way. Because of that, it is
difficult to realize the {\em logic} that is behind.
In this paper we introduce an original framework for Max-SAT that stresses
the parallelism with classical SAT. Then, we extend the two basic SAT solving
techniques: {\em search} and {\em inference}. We show that many algorithmic
{\em tricks} used in state-of-the-art Max-SAT solvers are easily expressable in
{\em logic} terms with our framework in a unified manner.
Besides, we introduce an original search algorithm that performs a restricted
amount of {\em weighted resolution} at each visited node. We empirically
compare our algorithm with a variety of solving alternatives on several
benchmarks. Our experiments, which constitute to the best of our knowledge the
most comprehensive Max-sat evaluation ever reported, show that our algorithm is
generally orders of magnitude faster than any competitor
Identifying Security-Critical Cyber-Physical Components in Industrial Control Systems
In recent years, Industrial Control Systems (ICS) have become an appealing
target for cyber attacks, having massive destructive consequences. Security
metrics are therefore essential to assess their security posture. In this
paper, we present a novel ICS security metric based on AND/OR graphs that
represent cyber-physical dependencies among network components. Our metric is
able to efficiently identify sets of critical cyber-physical components, with
minimal cost for an attacker, such that if compromised, the system would enter
into a non-operational state. We address this problem by efficiently
transforming the input AND/OR graph-based model into a weighted logical formula
that is then used to build and solve a Weighted Partial MAX-SAT problem. Our
tool, META4ICS, leverages state-of-the-art techniques from the field of logical
satisfiability optimisation in order to achieve efficient computation times.
Our experimental results indicate that the proposed security metric can
efficiently scale to networks with thousands of nodes and be computed in
seconds. In addition, we present a case study where we have used our system to
analyse the security posture of a realistic water transport network. We discuss
our findings on the plant as well as further security applications of our
metric.Comment: Keywords: Security metrics, industrial control systems,
cyber-physical systems, AND-OR graphs, MAX-SAT resolutio
Fuzzy Maximum Satisfiability
In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to
{\L}ukasiewicz logic. The MaxSAT problem for a set of formulae {\Phi} is the
problem of finding an assignment to the variables in {\Phi} that satisfies the
maximum number of formulae. Three possible solutions (encodings) are proposed
to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer
Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem
(WCSP). Like its Boolean counterpart, the extended fuzzy MaxSAT will have
numerous applications in optimization problems that involve vagueness.Comment: 10 page
On complexity of optimized crossover for binary representations
We consider the computational complexity of producing the best possible
offspring in a crossover, given two solutions of the parents. The crossover
operators are studied on the class of Boolean linear programming problems,
where the Boolean vector of variables is used as the solution representation.
By means of efficient reductions of the optimized gene transmitting crossover
problems (OGTC) we show the polynomial solvability of the OGTC for the maximum
weight set packing problem, the minimum weight set partition problem and for
one of the versions of the simple plant location problem. We study a connection
between the OGTC for linear Boolean programming problem and the maximum weight
independent set problem on 2-colorable hypergraph and prove the NP-hardness of
several special cases of the OGTC problem in Boolean linear programming.Comment: Dagstuhl Seminar 06061 "Theory of Evolutionary Algorithms", 200
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
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