97,882 research outputs found
New results on rewrite-based satisfiability procedures
Program analysis and verification require decision procedures to reason on
theories of data structures. Many problems can be reduced to the satisfiability
of sets of ground literals in theory T. If a sound and complete inference
system for first-order logic is guaranteed to terminate on T-satisfiability
problems, any theorem-proving strategy with that system and a fair search plan
is a T-satisfiability procedure. We prove termination of a rewrite-based
first-order engine on the theories of records, integer offsets, integer offsets
modulo and lists. We give a modularity theorem stating sufficient conditions
for termination on a combinations of theories, given termination on each. The
above theories, as well as others, satisfy these conditions. We introduce
several sets of benchmarks on these theories and their combinations, including
both parametric synthetic benchmarks to test scalability, and real-world
problems to test performances on huge sets of literals. We compare the
rewrite-based theorem prover E with the validity checkers CVC and CVC Lite.
Contrary to the folklore that a general-purpose prover cannot compete with
reasoners with built-in theories, the experiments are overall favorable to the
theorem prover, showing that not only the rewriting approach is elegant and
conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page
Doppler peaks from active perturbations
We examine how the qualitative structure of the Doppler peaks in the angular
power spectrum of the cosmic microwave anisotropy depends on the fundamental
nature of the perturbations which produced them. The formalism of Hu and
Sugiyama is extended to treat models with cosmic defects. We discuss how
perturbations can be ``active'' or ``passive'' and ``incoherent'' or
``coherent'', and show how causality and scale invariance play rather different
roles in these various cases. We find that the existence of secondary Doppler
peaks and the rough placing of the primary peak unambiguously reflect these
basic properties.Comment: uufile, 8pages, 3 figures. Now available at
http://euclid.tp.ph/Papers/index.html; Changes: URL added, Eqn. (8) expanded,
grant numbers include
The KB paradigm and its application to interactive configuration
The knowledge base paradigm aims to express domain knowledge in a rich formal
language, and to use this domain knowledge as a knowledge base to solve various
problems and tasks that arise in the domain by applying multiple forms of
inference. As such, the paradigm applies a strict separation of concerns
between information and problem solving. In this paper, we analyze the
principles and feasibility of the knowledge base paradigm in the context of an
important class of applications: interactive configuration problems. In
interactive configuration problems, a configuration of interrelated objects
under constraints is searched, where the system assists the user in reaching an
intended configuration. It is widely recognized in industry that good software
solutions for these problems are very difficult to develop. We investigate such
problems from the perspective of the KB paradigm. We show that multiple
functionalities in this domain can be achieved by applying different forms of
logical inferences on a formal specification of the configuration domain. We
report on a proof of concept of this approach in a real-life application with a
banking company. To appear in Theory and Practice of Logic Programming (TPLP).Comment: To appear in Theory and Practice of Logic Programming (TPLP
Induction of models under uncertainty
This paper outlines a procedure for performing induction under uncertainty. This procedure uses a probabilistic representation and uses Bayes' theorem to decide between alternative hypotheses (theories). This procedure is illustrated by a robot with no prior world experience performing induction on data it has gathered about the world. The particular inductive problem is the formation of class descriptions both for the tutored and untutored cases. The resulting class definitions are inherently probabilistic and so do not have any sharply defined membership criterion. This robot example raises some fundamental problems about induction; particularly, it is shown that inductively formed theories are not the best way to make predictions. Another difficulty is the need to provide prior probabilities for the set of possible theories. The main criterion for such priors is a pragmatic one aimed at keeping the theory structure as simple as possible, while still reflecting any structure discovered in the data
Games for the Strategic Influence of Expectations
We introduce a new class of games where each player's aim is to randomise her
strategic choices in order to affect the other players' expectations aside from
her own. The way each player intends to exert this influence is expressed
through a Boolean combination of polynomial equalities and inequalities with
rational coefficients. We offer a logical representation of these games as well
as a computational study of the existence of equilibria.Comment: In Proceedings SR 2014, arXiv:1404.041
The First-Order Theory of Sets with Cardinality Constraints is Decidable
We show that the decidability of the first-order theory of the language that
combines Boolean algebras of sets of uninterpreted elements with Presburger
arithmetic operations. We thereby disprove a recent conjecture that this theory
is undecidable. Our language allows relating the cardinalities of sets to the
values of integer variables, and can distinguish finite and infinite sets. We
use quantifier elimination to show the decidability and obtain an elementary
upper bound on the complexity.
Precise program analyses can use our decidability result to verify
representation invariants of data structures that use an integer field to
represent the number of stored elements.Comment: 18 page
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