3,614 research outputs found
Answer Sets for Logic Programs with Arbitrary Abstract Constraint Atoms
In this paper, we present two alternative approaches to defining answer sets
for logic programs with arbitrary types of abstract constraint atoms (c-atoms).
These approaches generalize the fixpoint-based and the level mapping based
answer set semantics of normal logic programs to the case of logic programs
with arbitrary types of c-atoms. The results are four different answer set
definitions which are equivalent when applied to normal logic programs. The
standard fixpoint-based semantics of logic programs is generalized in two
directions, called answer set by reduct and answer set by complement. These
definitions, which differ from each other in the treatment of
negation-as-failure (naf) atoms, make use of an immediate consequence operator
to perform answer set checking, whose definition relies on the notion of
conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The other
two definitions, called strongly and weakly well-supported models, are
generalizations of the notion of well-supported models of normal logic programs
to the case of programs with c-atoms. As for the case of fixpoint-based
semantics, the difference between these two definitions is rooted in the
treatment of naf atoms. We prove that answer sets by reduct (resp. by
complement) are equivalent to weakly (resp. strongly) well-supported models of
a program, thus generalizing the theorem on the correspondence between stable
models and well-supported models of a normal logic program to the class of
programs with c-atoms. We show that the newly defined semantics coincide with
previously introduced semantics for logic programs with monotone c-atoms, and
they extend the original answer set semantics of normal logic programs. We also
study some properties of answer sets of programs with c-atoms, and relate our
definitions to several semantics for logic programs with aggregates presented
in the literature
Generalization Strategies for the Verification of Infinite State Systems
We present a method for the automated verification of temporal properties of
infinite state systems. Our verification method is based on the specialization
of constraint logic programs (CLP) and works in two phases: (1) in the first
phase, a CLP specification of an infinite state system is specialized with
respect to the initial state of the system and the temporal property to be
verified, and (2) in the second phase, the specialized program is evaluated by
using a bottom-up strategy. The effectiveness of the method strongly depends on
the generalization strategy which is applied during the program specialization
phase. We consider several generalization strategies obtained by combining
techniques already known in the field of program analysis and program
transformation, and we also introduce some new strategies. Then, through many
verification experiments, we evaluate the effectiveness of the generalization
strategies we have considered. Finally, we compare the implementation of our
specialization-based verification method to other constraint-based model
checking tools. The experimental results show that our method is competitive
with the methods used by those other tools. To appear in Theory and Practice of
Logic Programming (TPLP).Comment: 24 pages, 2 figures, 5 table
Rewriting recursive aggregates in answer set programming: back to monotonicity
Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall performance. In particular, aggregates are rewritten into simpler forms known as monotone aggregates. Since the evaluation of normal programs with monotone aggregates is in general on a lower complexity level than the evaluation of normal programs with arbitrary aggregates, any faithful translation function must introduce disjunction in rule heads in some cases. However, no function of this kind is known. The paper closes this gap by introducing a polynomial, faithful, and modular translation for rewriting common aggregation functions into the simpler form accepted by current solvers. A prototype system allows for experimenting with arbitrary recursive aggregates, which are also supported in the recent version 4.5 of the grounder gringo, using the methods presented in this paper
Combining Forward and Backward Abstract Interpretation of Horn Clauses
Alternation of forward and backward analyses is a standard technique in
abstract interpretation of programs, which is in particular useful when we wish
to prove unreachability of some undesired program states. The current
state-of-the-art technique for combining forward (bottom-up, in logic
programming terms) and backward (top-down) abstract interpretation of Horn
clauses is query-answer transformation. It transforms a system of Horn clauses,
such that standard forward analysis can propagate constraints both forward, and
backward from a goal. Query-answer transformation is effective, but has issues
that we wish to address. For that, we introduce a new backward collecting
semantics, which is suitable for alternating forward and backward abstract
interpretation of Horn clauses. We show how the alternation can be used to
prove unreachability of the goal and how every subsequent run of an analysis
yields a refined model of the system. Experimentally, we observe that combining
forward and backward analyses is important for analysing systems that encode
questions about reachability in C programs. In particular, the combination that
follows our new semantics improves the precision of our own abstract
interpreter, including when compared to a forward analysis of a
query-answer-transformed system.Comment: Francesco Ranzato. 24th International Static Analysis Symposium
(SAS), Aug 2017, New York City, United States. Springer, Static Analysi
Posets arising as 1-skeleta of simple polytopes, the nonrevisiting path conjecture, and poset topology
Given any polytope and any generic linear functional , one
obtains a directed graph by taking the 1-skeleton of and
orienting each edge from to for .
This paper raises the question of finding sufficient conditions on a polytope
and generic cost vector so that the graph will
not have any directed paths which revisit any face of after departing from
that face. This is in a sense equivalent to the question of finding conditions
on and under which the simplex method for linear programming
will be efficient under all choices of pivot rules. Conditions on and are given which provably yield a corollary of the desired face
nonrevisiting property and which are conjectured to give the desired property
itself. This conjecture is proven for 3-polytopes and for spindles having the
two distinguished vertices as source and sink; this shows that known
counterexamples to the Hirsch Conjecture will not provide counterexamples to
this conjecture.
A part of the proposed set of conditions is that be the
Hasse diagram of a partially ordered set, which is equivalent to requiring non
revisiting of 1-dimensional faces. This opens the door to the usage of
poset-theoretic techniques. This work also leads to a result for simple
polytopes in which is the Hasse diagram of a lattice L that the
order complex of each open interval in L is homotopy equivalent to a ball or a
sphere of some dimension. Applications are given to the weak Bruhat order, the
Tamari lattice, and more generally to the Cambrian lattices, using realizations
of the Hasse diagrams of these posets as 1-skeleta of permutahedra,
associahedra, and generalized associahedra.Comment: new results for 3-polytopes and spindles added; exposition
substantially improved throughou
Logic Integer Programming Models for Signaling Networks
We propose a static and a dynamic approach to model biological signaling
networks, and show how each can be used to answer relevant biological
questions. For this we use the two different mathematical tools of
Propositional Logic and Integer Programming. The power of discrete mathematics
for handling qualitative as well as quantitative data has so far not been
exploited in Molecular Biology, which is mostly driven by experimental
research, relying on first-order or statistical models. The arising logic
statements and integer programs are analyzed and can be solved with standard
software. For a restricted class of problems the logic models reduce to a
polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic
model enables enumeration of possible time resolutions in poly-logarithmic
time. Computational experiments are included
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