12,196 research outputs found
A Framework for Consistency Algorithms
We present a framework that provides deterministic consistency algorithms for given memory models. Such an algorithm checks whether the executions of a shared-memory concurrent program are consistent under the axioms defined by a model. For memory models like SC and TSO, checking consistency is NP-complete. Our framework shows, that despite the hardness, fast deterministic consistency algorithms can be obtained by employing tools from fine-grained complexity.
The framework is based on a universal consistency problem which can be instantiated by different memory models. We construct an algorithm for the problem running in time ?^*(2^k), where k is the number of write accesses in the execution that is checked for consistency. Each instance of the framework then admits an ?^*(2^k)-time consistency algorithm. By applying the framework, we obtain corresponding consistency algorithms for SC, TSO, PSO, and RMO. Moreover, we show that the obtained algorithms for SC, TSO, and PSO are optimal in the fine-grained sense: there is no consistency algorithm for these running in time 2^{o(k)} unless the exponential time hypothesis fails
On model checking data-independent systems with arrays without reset
A system is data-independent with respect to a data type X iff the operations
it can perform on values of type X are restricted to just equality testing. The
system may also store, input and output values of type X. We study model
checking of systems which are data-independent with respect to two distinct
type variables X and Y, and may in addition use arrays with indices from X and
values from Y . Our main interest is the following parameterised model-checking
problem: whether a given program satisfies a given temporal-logic formula for
all non-empty nite instances of X and Y . Initially, we consider instead the
abstraction where X and Y are infinite and where partial functions with finite
domains are used to model arrays. Using a translation to data-independent
systems without arrays, we show that the u-calculus model-checking problem is
decidable for these systems. From this result, we can deduce properties of all
systems with finite instances of X and Y . We show that there is a procedure
for the above parameterised model-checking problem of the universal fragment of
the u-calculus, such that it always terminates but may give false negatives. We
also deduce that the parameterised model-checking problem of the universal
disjunction-free fragment of the u-calculus is decidable. Practical motivations
for model checking data-independent systems with arrays include verification of
memory and cache systems, where X is the type of memory addresses, and Y the
type of storable values. As an example we verify a fault-tolerant memory
interface over a set of unreliable memories.Comment: Appeared in Theory and Practice of Logic Programming, vol. 4, no.
5&6, 200
Proving sequential consistency by model checking
Sequential consistency is a multiprocessor memory model of both practical and theoretical importance. Unfortunately, the general problem of verifying that a finitestate protocol implements sequential consistency is undecidable, and in practice, validating that a real-world, finitestate protocol implements sequential consistency is very time-consuming and costly. In this work, we show that for memory protocols that occur in practice, a small amount of manual effort can reduce the problem of verifying sequential consistency into a verification task that can be discharged automatically via model checking. Furthermore, we present experimental results on a substantial, directorybased cache coherence protocol, which demonstrate the practicality of our approach.
Verification of a lazy cache coherence protocol against a weak memory model
In this paper we verify a modern lazy cache coherence protocol, TSO-CC,
against the memory consistency model it was designed for, TSO. We achieve this
by first showing a weak simulation relation between TSO-CC (with a fixed number
of processors) and a novel finite-state operational model which exhibits the
laziness of TSO-CC and satisfies TSO. We then extend this by an existing
parameterisation technique, allowing verification for an unlimited number of
processors. The approach is executed entirely within a model checker, no
external tool is required and very little in-depth knowledge of formal
verification methods is required of the verifier.Comment: 10 page
Predicate Abstraction with Indexed Predicates
Predicate abstraction provides a powerful tool for verifying properties of
infinite-state systems using a combination of a decision procedure for a subset
of first-order logic and symbolic methods originally developed for finite-state
model checking. We consider models containing first-order state variables,
where the system state includes mutable functions and predicates. Such a model
can describe systems containing arbitrarily large memories, buffers, and arrays
of identical processes. We describe a form of predicate abstraction that
constructs a formula over a set of universally quantified variables to describe
invariant properties of the first-order state variables. We provide a formal
justification of the soundness of our approach and describe how it has been
used to verify several hardware and software designs, including a
directory-based cache coherence protocol.Comment: 27 pages, 4 figures, 1 table, short version appeared in International
Conference on Verification, Model Checking and Abstract Interpretation
(VMCAI'04), LNCS 2937, pages = 267--28
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