14,860 research outputs found
Abstract Learning Frameworks for Synthesis
We develop abstract learning frameworks (ALFs) for synthesis that embody the
principles of CEGIS (counter-example based inductive synthesis) strategies that
have become widely applicable in recent years. Our framework defines a general
abstract framework of iterative learning, based on a hypothesis space that
captures the synthesized objects, a sample space that forms the space on which
induction is performed, and a concept space that abstractly defines the
semantics of the learning process. We show that a variety of synthesis
algorithms in current literature can be embedded in this general framework.
While studying these embeddings, we also generalize some of the synthesis
problems these instances are of, resulting in new ways of looking at synthesis
problems using learning. We also investigate convergence issues for the general
framework, and exhibit three recipes for convergence in finite time. The first
two recipes generalize current techniques for convergence used by existing
synthesis engines. The third technique is a more involved technique of which we
know of no existing instantiation, and we instantiate it to concrete synthesis
problems
The Hardness of Finding Linear Ranking Functions for Lasso Programs
Finding whether a linear-constraint loop has a linear ranking function is an
important key to understanding the loop behavior, proving its termination and
establishing iteration bounds. If no preconditions are provided, the decision
problem is known to be in coNP when variables range over the integers and in
PTIME for the rational numbers, or real numbers. Here we show that deciding
whether a linear-constraint loop with a precondition, specifically with
partially-specified input, has a linear ranking function is EXPSPACE-hard over
the integers, and PSPACE-hard over the rationals. The precise complexity of
these decision problems is yet unknown. The EXPSPACE lower bound is derived
from the reachability problem for Petri nets (equivalently, Vector Addition
Systems), and possibly indicates an even stronger lower bound (subject to open
problems in VAS theory). The lower bound for the rationals follows from a novel
simulation of Boolean programs. Lower bounds are also given for the problem of
deciding if a linear ranking-function supported by a particular form of
inductive invariant exists. For loops over integers, the problem is PSPACE-hard
for convex polyhedral invariants and EXPSPACE-hard for downward-closed sets of
natural numbers as invariants.Comment: In Proceedings GandALF 2014, arXiv:1408.5560. I thank the organizers
of the Dagstuhl Seminar 14141, "Reachability Problems for Infinite-State
Systems", for the opportunity to present an early draft of this wor
The JKind Model Checker
JKind is an open-source industrial model checker developed by Rockwell
Collins and the University of Minnesota. JKind uses multiple parallel engines
to prove or falsify safety properties of infinite state models. It is portable,
easy to install, performance competitive with other state-of-the-art model
checkers, and has features designed to improve the results presented to users:
inductive validity cores for proofs and counterexample smoothing for test-case
generation. It serves as the back-end for various industrial applications.Comment: CAV 201
A Generic Framework for Reasoning about Dynamic Networks of Infinite-State Processes
We propose a framework for reasoning about unbounded dynamic networks of
infinite-state processes. We propose Constrained Petri Nets (CPN) as generic
models for these networks. They can be seen as Petri nets where tokens
(representing occurrences of processes) are colored by values over some
potentially infinite data domain such as integers, reals, etc. Furthermore, we
define a logic, called CML (colored markings logic), for the description of CPN
configurations. CML is a first-order logic over tokens allowing to reason about
their locations and their colors. Both CPNs and CML are parametrized by a color
logic allowing to express constraints on the colors (data) associated with
tokens. We investigate the decidability of the satisfiability problem of CML
and its applications in the verification of CPNs. We identify a fragment of CML
for which the satisfiability problem is decidable (whenever it is the case for
the underlying color logic), and which is closed under the computations of post
and pre images for CPNs. These results can be used for several kinds of
analysis such as invariance checking, pre-post condition reasoning, and bounded
reachability analysis.Comment: 29 pages, 5 tables, 1 figure, extended version of the paper published
in the the Proceedings of TACAS 2007, LNCS 442
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