177,707 research outputs found
On optimizing over lift-and-project closures
The lift-and-project closure is the relaxation obtained by computing all
lift-and-project cuts from the initial formulation of a mixed integer linear
program or equivalently by computing all mixed integer Gomory cuts read from
all tableau's corresponding to feasible and infeasible bases. In this paper, we
present an algorithm for approximating the value of the lift-and-project
closure. The originality of our method is that it is based on a very simple cut
generation linear programming problem which is obtained from the original
linear relaxation by simply modifying the bounds on the variables and
constraints. This separation LP can also be seen as the dual of the cut
generation LP used in disjunctive programming procedures with a particular
normalization. We study some properties of this separation LP in particular
relating it to the equivalence between lift-and-project cuts and Gomory cuts
shown by Balas and Perregaard. Finally, we present some computational
experiments and comparisons with recent related works
Organisational closure in biological organisms
International audienceThe central aim of this paper consists in arguing that biological organisms realize a specific kind of causal regime that we call "organisational closure"; i.e., a distinct level of causation, operating in addition to physical laws, generated by the action of material structures acting as constraints. We argue that organisational closure constitutes a fundamental property of biological systems since even its minimal instances are likely to possess at least some of the typical features of biological organisation as exhibited by more complex organisms. Yet, while being a necessary condition for biological organization, organisational closure underdetermines, as such, the whole set of requirements that a system has to satisfy in order to be taken as a paradigmatic example of organism. As we suggest, additional properties, as modular templates and control mechanisms via dynamical decoupling between constraints, are required to get the complexity typical of full-fledged biological organisms
Model Checking Synchronized Products of Infinite Transition Systems
Formal verification using the model checking paradigm has to deal with two
aspects: The system models are structured, often as products of components, and
the specification logic has to be expressive enough to allow the formalization
of reachability properties. The present paper is a study on what can be
achieved for infinite transition systems under these premises. As models we
consider products of infinite transition systems with different synchronization
constraints. We introduce finitely synchronized transition systems, i.e.
product systems which contain only finitely many (parameterized) synchronized
transitions, and show that the decidability of FO(R), first-order logic
extended by reachability predicates, of the product system can be reduced to
the decidability of FO(R) of the components. This result is optimal in the
following sense: (1) If we allow semifinite synchronization, i.e. just in one
component infinitely many transitions are synchronized, the FO(R)-theory of the
product system is in general undecidable. (2) We cannot extend the expressive
power of the logic under consideration. Already a weak extension of first-order
logic with transitive closure, where we restrict the transitive closure
operators to arity one and nesting depth two, is undecidable for an
asynchronous (and hence finitely synchronized) product, namely for the infinite
grid.Comment: 18 page
Tree Automata with Global Constraints for Infinite Trees
We study an extension of tree automata on infinite trees with global equality and disequality constraints. These constraints can enforce that all subtrees for which in the accepting run a state q is reached (at the root of that subtree) are identical, or that these trees differ from the subtrees at which a state q\u27 is reached. We consider the closure properties of this model and its decision problems. While the emptiness problem for the general model remains open, we show the decidability of the emptiness problem for the case that the given automaton only uses equality constraints
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Tier-Based Strictly Local Stringsets: Perspectives from Model and Automata Theory
Defined by Heinz et al. (2011) the Tier-Based Strictly Local (TSL) class of stringsets has not previously been characterized by an abstract property that allows one to prove a stringset\u27s membership or lack thereof. We provide here two such characterizations: a generalization of suffix substitution closure and an algorithm based on deterministic finite-state automata (DFAs). We use the former to prove closure properties of the class. Additionally, we extend the approximation and constraint-extraction algorithms of Rogers and Lambert (2019a) to account for TSL constraints, allowing for free conversion between TSL logical formulae and DFAs
On Role Logic
We present role logic, a notation for describing properties of relational
structures in shape analysis, databases, and knowledge bases. We construct role
logic using the ideas of de Bruijn's notation for lambda calculus, an encoding
of first-order logic in lambda calculus, and a simple rule for implicit
arguments of unary and binary predicates. The unrestricted version of role
logic has the expressive power of first-order logic with transitive closure.
Using a syntactic restriction on role logic formulas, we identify a natural
fragment RL^2 of role logic. We show that the RL^2 fragment has the same
expressive power as two-variable logic with counting C^2 and is therefore
decidable. We present a translation of an imperative language into the
decidable fragment RL^2, which allows compositional verification of programs
that manipulate relational structures. In addition, we show how RL^2 encodes
boolean shape analysis constraints and an expressive description logic.Comment: 20 pages. Our later SAS 2004 result builds on this wor
Growing Attributed Networks through Local Processes
This paper proposes an attributed network growth model. Despite the knowledge
that individuals use limited resources to form connections to similar others,
we lack an understanding of how local and resource-constrained mechanisms
explain the emergence of rich structural properties found in real-world
networks. We make three contributions. First, we propose a parsimonious and
accurate model of attributed network growth that jointly explains the emergence
of in-degree distributions, local clustering, clustering-degree relationship
and attribute mixing patterns. Second, our model is based on biased random
walks and uses local processes to form edges without recourse to global network
information. Third, we account for multiple sociological phenomena: bounded
rationality, structural constraints, triadic closure, attribute homophily, and
preferential attachment. Our experiments indicate that the proposed Attributed
Random Walk (ARW) model accurately preserves network structure and attribute
mixing patterns of six real-world networks; it improves upon the performance of
eight state-of-the-art models by a statistically significant margin of 2.5-10x.Comment: 11 pages, 13 figure
Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data
Constraint Programming (CP) has proved an effective paradigm to model and
solve difficult combinatorial satisfaction and optimisation problems from
disparate domains. Many such problems arising from the commercial world are
permeated by data uncertainty. Existing CP approaches that accommodate
uncertainty are less suited to uncertainty arising due to incomplete and
erroneous data, because they do not build reliable models and solutions
guaranteed to address the user's genuine problem as she perceives it. Other
fields such as reliable computation offer combinations of models and associated
methods to handle these types of uncertain data, but lack an expressive
framework characterising the resolution methodology independently of the model.
We present a unifying framework that extends the CP formalism in both model
and solutions, to tackle ill-defined combinatorial problems with incomplete or
erroneous data. The certainty closure framework brings together modelling and
solving methodologies from different fields into the CP paradigm to provide
reliable and efficient approches for uncertain constraint problems. We
demonstrate the applicability of the framework on a case study in network
diagnosis. We define resolution forms that give generic templates, and their
associated operational semantics, to derive practical solution methods for
reliable solutions.Comment: Revised versio
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