719 research outputs found
Symmetry Breaking for Answer Set Programming
In the context of answer set programming, this work investigates symmetry
detection and symmetry breaking to eliminate symmetric parts of the search
space and, thereby, simplify the solution process. We contribute a reduction of
symmetry detection to a graph automorphism problem which allows to extract
symmetries of a logic program from the symmetries of the constructed coloured
graph. We also propose an encoding of symmetry-breaking constraints in terms of
permutation cycles and use only generators in this process which implicitly
represent symmetries and always with exponential compression. These ideas are
formulated as preprocessing and implemented in a completely automated flow that
first detects symmetries from a given answer set program, adds
symmetry-breaking constraints, and can be applied to any existing answer set
solver. We demonstrate computational impact on benchmarks versus direct
application of the solver.
Furthermore, we explore symmetry breaking for answer set programming in two
domains: first, constraint answer set programming as a novel approach to
represent and solve constraint satisfaction problems, and second, distributed
nonmonotonic multi-context systems. In particular, we formulate a
translation-based approach to constraint answer set solving which allows for
the application of our symmetry detection and symmetry breaking methods. To
compare their performance with a-priori symmetry breaking techniques, we also
contribute a decomposition of the global value precedence constraint that
enforces domain consistency on the original constraint via the unit-propagation
of an answer set solver. We evaluate both options in an empirical analysis. In
the context of distributed nonmonotonic multi-context system, we develop an
algorithm for distributed symmetry detection and also carry over
symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201
Transfer Function Synthesis without Quantifier Elimination
Traditionally, transfer functions have been designed manually for each
operation in a program, instruction by instruction. In such a setting, a
transfer function describes the semantics of a single instruction, detailing
how a given abstract input state is mapped to an abstract output state. The net
effect of a sequence of instructions, a basic block, can then be calculated by
composing the transfer functions of the constituent instructions. However,
precision can be improved by applying a single transfer function that captures
the semantics of the block as a whole. Since blocks are program-dependent, this
approach necessitates automation. There has thus been growing interest in
computing transfer functions automatically, most notably using techniques based
on quantifier elimination. Although conceptually elegant, quantifier
elimination inevitably induces a computational bottleneck, which limits the
applicability of these methods to small blocks. This paper contributes a method
for calculating transfer functions that finesses quantifier elimination
altogether, and can thus be seen as a response to this problem. The
practicality of the method is demonstrated by generating transfer functions for
input and output states that are described by linear template constraints,
which include intervals and octagons.Comment: 37 pages, extended version of ESOP 2011 pape
Symmetry-breaking Answer Set Solving
In the context of Answer Set Programming, this paper investigates
symmetry-breaking to eliminate symmetric parts of the search space and,
thereby, simplify the solution process. We propose a reduction of disjunctive
logic programs to a coloured digraph such that permutational symmetries can be
constructed from graph automorphisms. Symmetries are then broken by introducing
symmetry-breaking constraints. For this purpose, we formulate a preprocessor
that integrates a graph automorphism system. Experiments demonstrate its
computational impact.Comment: Proceedings of ICLP'10 Workshop on Answer Set Programming and Other
Computing Paradig
Scalable Verification of Quantized Neural Networks (Technical Report)
Formal verification of neural networks is an active topic of research, and
recent advances have significantly increased the size of the networks that
verification tools can handle. However, most methods are designed for
verification of an idealized model of the actual network which works over real
arithmetic and ignores rounding imprecisions. This idealization is in stark
contrast to network quantization, which is a technique that trades numerical
precision for computational efficiency and is, therefore, often applied in
practice. Neglecting rounding errors of such low-bit quantized neural networks
has been shown to lead to wrong conclusions about the network's correctness.
Thus, the desired approach for verifying quantized neural networks would be one
that takes these rounding errors into account. In this paper, we show that
verifying the bit-exact implementation of quantized neural networks with
bit-vector specifications is PSPACE-hard, even though verifying idealized
real-valued networks and satisfiability of bit-vector specifications alone are
each in NP. Furthermore, we explore several practical heuristics toward closing
the complexity gap between idealized and bit-exact verification. In particular,
we propose three techniques for making SMT-based verification of quantized
neural networks more scalable. Our experiments demonstrate that our proposed
methods allow a speedup of up to three orders of magnitude over existing
approaches
Z2SAL: a translation-based model checker for Z
Despite being widely known and accepted in industry, the Z formal specification language has not so far been well supported by automated verification tools, mostly because of the challenges in handling the abstraction of the language. In this paper we discuss a novel approach to building a model-checker for Z, which involves implementing a translation from Z into SAL, the input language for the Symbolic Analysis Laboratory, a toolset which includes a number of model-checkers and a simulator. The Z2SAL translation deals with a number of important issues, including: mapping unbounded, abstract specifications into bounded, finite models amenable to a BDD-based symbolic checker; converting a non-constructive and piecemeal style of functional specification into a deterministic, automaton-based style of specification; and supporting the rich set-based vocabulary of the Z mathematical toolkit. This paper discusses progress made towards implementing as complete and faithful a translation as possible, while highlighting certain assumptions, respecting certain limitations and making use of available optimisations. The translation is illustrated throughout with examples; and a complete working example is presented, together with performance data
Solving hard industrial combinatorial problems with SAT
The topic of this thesis is the development of SAT-based techniques and tools for solving industrial combinatorial problems. First, it describes the architecture of state-of-the-art SAT and SMT Solvers based on the classical DPLL procedure. These systems can be used as black boxes for solving combinatorial problems. However, sometimes we can increase their efficiency with slight modifications of the basic algorithm. Therefore, the study and development of techniques for adjusting SAT Solvers to specific combinatorial problems is the first goal of this thesis.
Namely, SAT Solvers can only deal with propositional logic. For solving general combinatorial problems, two different approaches are possible:
- Reducing the complex constraints into propositional clauses.
- Enriching the SAT Solver language.
The first approach corresponds to encoding the constraint into SAT. The second one corresponds to using propagators, the basis for SMT Solvers. Regarding the first approach, in this document we improve the encoding of two of the most important combinatorial constraints: cardinality constraints and pseudo-Boolean constraints. After that, we present a new mixed approach, called lazy decomposition, which combines the advantages of encodings and propagators.
The other part of the thesis uses these theoretical improvements in industrial combinatorial problems. We give a method for efficiently scheduling some professional sport leagues with SAT. The results are promising and show that a SAT approach is valid for these problems.
However, the chaotical behavior of CDCL-based SAT Solvers due to VSIDS heuristics makes it difficult to obtain a similar solution for two similar problems. This may be inconvenient in real-world problems, since a user expects similar solutions when it makes slight modifications to the problem specification. In order to overcome this limitation, we have studied and solved the close solution problem, i.e., the problem of quickly finding a close solution when a similar problem is considered
The Impact of Implied Constraints on MaxSAT B2B Instances
The B2B scheduling optimization problem consists of finding a schedule of a set of meetings between pairs of participants,
minimizing their number of idle time periods. Recent works have shown that SAT-based approaches are state-of-the-art
on this problem. One interesting feature of such approaches is the use of implied constraints. In this work, we provide an
experimental setting to study the impact of using these implied constraints in MaxSAT B2B instances. To this purpose and
due to the reduced number of existing real-world B2B instances, we propose a random B2B instance generation model,
which reproduces certain features of these problems. In our experimental analysis, we show that the impact of using some
implied constraints in the MaxSAT encodings depends on the characteristics of the problem, and we also analyze the benefits
of combining them. Finally, we give some insights on how a MaxSAT solver is able to exploit these implied constraints.Spanish Government RTI2018-095609-B-I00French National Research Agency (ANR) ANR-19-CHIA-0013-01Juan de la Cierva program - MCIN IJC2019040489-IAE
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