18,535 research outputs found
Lazy Shape Analysis
Many software model checkers are based on predicate abstraction. If
the verification goal depends on pointer structures, the approach does
not work well, because it is difficult to find adequate predicate
abstractions for the heap. In contrast, shape analysis, which uses
graph-based heap abstractions, can provide a compact representation of
recursive data structures. We integrate shape analysis into the
software model checker BLAST. Because shape analysis is expensive, we
do not apply it globally. Instead, we ensure that, like predicates,
shape graphs are computed and stored locally, only where necessary for
proving the verification goal. To achieve this, we extend lazy
abstraction refinement, which so far has been used only for predicate
abstractions, to three-valued logical structures. This approach does
not only increase the precision of model checking, but it also
increases the efficiency of shape analysis. We implemented the
technique by extending BLAST with calls to TVLA
Integrating Shape Analysis into the Model Checker BLAST
Many software model checkers are based on predicate abstraction. Values of variables in branching conditions are represented abstractly using predicates. The strength of this approach is its path-sensitive nature. However, if the control flow depends heavily on the values of memory cells on the heap, the approach does not work well, because it is difficult to find `good' predicate abstractions to represent the heap. In contrast, shape analysis can lead to a very compact representation of data structures stored on the heap. In this thesis, we combine shape analysis with predicate abstraction, and integrate it into the software model checker BLAST. Because shape analysis is expensive, we do not apply it globally. Instead, we ensure that shapes are computed and stored locally, only where necessary for proving the verification goal. To achieve this, we extend lazy abstraction refinement, which so far has been used only for predicate abstractions, to shapes. This approach does not only increase the precision of model checking and shape analysis taken individually, but also increases the efficiency of shape analysis (we do not compute shapes where not necessary). We implemented the technique by extending BLAST with calls to TVLA, and evaluated it on several C programs manipulating data structures, with the result that the combined tool can now automatically verify programs that are not verifiable using either shape analysis or predicate abstraction on its own
Predicate Abstraction for Linked Data Structures
We present Alias Refinement Types (ART), a new approach to the verification
of correctness properties of linked data structures. While there are many
techniques for checking that a heap-manipulating program adheres to its
specification, they often require that the programmer annotate the behavior of
each procedure, for example, in the form of loop invariants and pre- and
post-conditions. Predicate abstraction would be an attractive abstract domain
for performing invariant inference, existing techniques are not able to reason
about the heap with enough precision to verify functional properties of data
structure manipulating programs. In this paper, we propose a technique that
lifts predicate abstraction to the heap by factoring the analysis of data
structures into two orthogonal components: (1) Alias Types, which reason about
the physical shape of heap structures, and (2) Refinement Types, which use
simple predicates from an SMT decidable theory to capture the logical or
semantic properties of the structures. We prove ART sound by translating types
into separation logic assertions, thus translating typing derivations in ART
into separation logic proofs. We evaluate ART by implementing a tool that
performs type inference for an imperative language, and empirically show, using
a suite of data-structure benchmarks, that ART requires only 21% of the
annotations needed by other state-of-the-art verification techniques
On Verifying Complex Properties using Symbolic Shape Analysis
One of the main challenges in the verification of software systems is the
analysis of unbounded data structures with dynamic memory allocation, such as
linked data structures and arrays. We describe Bohne, a new analysis for
verifying data structures. Bohne verifies data structure operations and shows
that 1) the operations preserve data structure invariants and 2) the operations
satisfy their specifications expressed in terms of changes to the set of
objects stored in the data structure. During the analysis, Bohne infers loop
invariants in the form of disjunctions of universally quantified Boolean
combinations of formulas. To synthesize loop invariants of this form, Bohne
uses a combination of decision procedures for Monadic Second-Order Logic over
trees, SMT-LIB decision procedures (currently CVC Lite), and an automated
reasoner within the Isabelle interactive theorem prover. This architecture
shows that synthesized loop invariants can serve as a useful communication
mechanism between different decision procedures. Using Bohne, we have verified
operations on data structures such as linked lists with iterators and back
pointers, trees with and without parent pointers, two-level skip lists, array
data structures, and sorted lists. We have deployed Bohne in the Hob and Jahob
data structure analysis systems, enabling us to combine Bohne with analyses of
data structure clients and apply it in the context of larger programs. This
report describes the Bohne algorithm as well as techniques that Bohne uses to
reduce the ammount of annotations and the running time of the analysis
Shape predicates allow unbounded verification of linearizability using canonical abstraction
Canonical abstraction is a static analysis technique that represents states as 3-valued logical structures, and is able to construct finite representations of systems with infinite statespaces for verification. The granularity of the abstraction can be altered by the definition of instrumentation predicates, which derive their meaning from other predicates. We introduce shape predicates for preserving certain structures of the state during abstraction. We show that shape predicates allow linearizability to be verified for concurrent data structures using canonical abstraction alone, and use the approach to verify a stack and two queue algorithms. This contrasts with previous efforts to verify linearizability with canonical abstraction, which have had to employ other techniques as well
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
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