22,164 research outputs found
On Model Checking Boolean BI
The logic of bunched implications (BI), introduced by O'Hearn and Pym, is a substructural logic which freely combines additive and multiplicative implications. Boolean BI (BBI) denotes BI with classical interpretation of additives and its model is the commutative monoid. We show that when the monoid is finitely generated and propositions are recursively defined, or the monoid is infinitely generated and propositions are restricted to generator propositions, the model checking problem is undecidable. In the case of finitely related monoid and,generator propositions. the model checking problem is EXPSPACE-complete.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000270711900021&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Computer Science, Theory & MethodsEICPCI-S(ISTP)
Safety Model Checking with Complementary Approximations
Formal verification techniques such as model checking, are becoming popular
in hardware design. SAT-based model checking techniques such as IC3/PDR, have
gained a significant success in hardware industry. In this paper, we present a
new framework for SAT-based safety model checking, named Complementary
Approximate Reachability (CAR). CAR is based on standard reachability analysis,
but instead of maintaining a single sequence of reachable- state sets, CAR
maintains two sequences of over- and under- approximate reachable-state sets,
checking safety and unsafety at the same time. To construct the two sequences,
CAR uses standard Boolean-reasoning algorithms, based on satisfiability
solving, one to find a satisfying cube of a satisfiable Boolean formula, and
one to provide a minimal unsatisfiable core of an unsatisfiable Boolean
formula. We applied CAR to 548 hardware model-checking instances, and compared
its performance with IC3/PDR. Our results show that CAR is able to solve 42
instances that cannot be solved by IC3/PDR. When evaluated against a portfolio
that includes IC3/PDR and other approaches, CAR is able to solve 21 instances
that the other approaches cannot solve. We conclude that CAR should be
considered as a valuable member of any algorithmic portfolio for safety model
checking
Modal µ-Calculus, Model Checking and Gauß Elimination
In this paper we present a novel approach for solving Boolean equation systems with nested minimal and maximal fixpoints. The method works by successively eliminating variables and reducing a Boolean equation system similar to Gauß elimination for linear equation systems. It does not require backtracking techniques. Within one framework we suggest a global and a local algorithm. In the context of model checking in the modal-calculus the local algorithm is related to the tableau methods, but has a better worst case complexity
A Metric Encoding for Bounded Model Checking (extended version)
In Bounded Model Checking both the system model and the checked property are
translated into a Boolean formula to be analyzed by a SAT-solver. We introduce
a new encoding technique which is particularly optimized for managing
quantitative future and past metric temporal operators, typically found in
properties of hard real time systems. The encoding is simple and intuitive in
principle, but it is made more complex by the presence, typical of the Bounded
Model Checking technique, of backward and forward loops used to represent an
ultimately periodic infinite domain by a finite structure. We report and
comment on the new encoding technique and on an extensive set of experiments
carried out to assess its feasibility and effectiveness
Complexity of ITL model checking: some well-behaved fragments of the interval logic HS
Model checking has been successfully used in many computer science fields,
including artificial intelligence, theoretical computer science, and databases.
Most of the proposed solutions make use of classical, point-based temporal
logics, while little work has been done in the interval temporal logic setting.
Recently, a non-elementary model checking algorithm for Halpern and Shoham's
modal logic of time intervals HS over finite Kripke structures (under the
homogeneity assumption) and an EXPSPACE model checking procedure for two
meaningful fragments of it have been proposed. In this paper, we show that more
efficient model checking procedures can be developed for some expressive enough
fragments of HS
The model checking fingerprints of CTL operators
The aim of this study is to understand the inherent expressive power of CTL
operators. We investigate the complexity of model checking for all CTL
fragments with one CTL operator and arbitrary Boolean operators. This gives us
a fingerprint of each CTL operator. The comparison between the fingerprints
yields a hierarchy of the operators that mirrors their strength with respect to
model checking
Near-Optimal Scheduling for LTL with Future Discounting
We study the search problem for optimal schedulers for the linear temporal
logic (LTL) with future discounting. The logic, introduced by Almagor, Boker
and Kupferman, is a quantitative variant of LTL in which an event in the far
future has only discounted contribution to a truth value (that is a real number
in the unit interval [0, 1]). The precise problem we study---it naturally
arises e.g. in search for a scheduler that recovers from an internal error
state as soon as possible---is the following: given a Kripke frame, a formula
and a number in [0, 1] called a margin, find a path of the Kripke frame that is
optimal with respect to the formula up to the prescribed margin (a truly
optimal path may not exist). We present an algorithm for the problem; it works
even in the extended setting with propositional quality operators, a setting
where (threshold) model-checking is known to be undecidable
Ackermann Encoding, Bisimulations, and OBDDs
We propose an alternative way to represent graphs via OBDDs based on the
observation that a partition of the graph nodes allows sharing among the
employed OBDDs. In the second part of the paper we present a method to compute
at the same time the quotient w.r.t. the maximum bisimulation and the OBDD
representation of a given graph. The proposed computation is based on an
OBDD-rewriting of the notion of Ackermann encoding of hereditarily finite sets
into natural numbers.Comment: To appear on 'Theory and Practice of Logic Programming
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