8,312 research outputs found
Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking
One technique to reduce the state-space explosion problem in temporal logic
model checking is symmetry reduction. The combination of symmetry reduction and
symbolic model checking by using BDDs suffered a long time from the
prohibitively large BDD for the orbit relation. Dynamic symmetry reduction
calculates representatives of equivalence classes of states dynamically and
thus avoids the construction of the orbit relation. In this paper, we present a
new efficient model checking algorithm based on dynamic symmetry reduction. Our
experiments show that the algorithm is very fast and allows the verification of
larger systems. We additionally implemented the use of state symmetries for
symbolic symmetry reduction. To our knowledge we are the first who investigated
state symmetries in combination with BDD based symbolic model checking
Taming Numbers and Durations in the Model Checking Integrated Planning System
The Model Checking Integrated Planning System (MIPS) is a temporal least
commitment heuristic search planner based on a flexible object-oriented
workbench architecture. Its design clearly separates explicit and symbolic
directed exploration algorithms from the set of on-line and off-line computed
estimates and associated data structures. MIPS has shown distinguished
performance in the last two international planning competitions. In the last
event the description language was extended from pure propositional planning to
include numerical state variables, action durations, and plan quality objective
functions. Plans were no longer sequences of actions but time-stamped
schedules. As a participant of the fully automated track of the competition,
MIPS has proven to be a general system; in each track and every benchmark
domain it efficiently computed plans of remarkable quality. This article
introduces and analyzes the most important algorithmic novelties that were
necessary to tackle the new layers of expressiveness in the benchmark problems
and to achieve a high level of performance. The extensions include critical
path analysis of sequentially generated plans to generate corresponding optimal
parallel plans. The linear time algorithm to compute the parallel plan bypasses
known NP hardness results for partial ordering by scheduling plans with respect
to the set of actions and the imposed precedence relations. The efficiency of
this algorithm also allows us to improve the exploration guidance: for each
encountered planning state the corresponding approximate sequential plan is
scheduled. One major strength of MIPS is its static analysis phase that grounds
and simplifies parameterized predicates, functions and operators, that infers
knowledge to minimize the state description length, and that detects domain
object symmetries. The latter aspect is analyzed in detail. MIPS has been
developed to serve as a complete and optimal state space planner, with
admissible estimates, exploration engines and branching cuts. In the
competition version, however, certain performance compromises had to be made,
including floating point arithmetic, weighted heuristic search exploration
according to an inadmissible estimate and parameterized optimization
Symbolic Reachability Analysis of B through ProB and LTSmin
We present a symbolic reachability analysis approach for B that can provide a
significant speedup over traditional explicit state model checking. The
symbolic analysis is implemented by linking ProB to LTSmin, a high-performance
language independent model checker. The link is achieved via LTSmin's PINS
interface, allowing ProB to benefit from LTSmin's analysis algorithms, while
only writing a few hundred lines of glue-code, along with a bridge between ProB
and C using ZeroMQ. ProB supports model checking of several formal
specification languages such as B, Event-B, Z and TLA. Our experiments are
based on a wide variety of B-Method and Event-B models to demonstrate the
efficiency of the new link. Among the tested categories are state space
generation and deadlock detection; but action detection and invariant checking
are also feasible in principle. In many cases we observe speedups of several
orders of magnitude. We also compare the results with other approaches for
improving model checking, such as partial order reduction or symmetry
reduction. We thus provide a new scalable, symbolic analysis algorithm for the
B-Method and Event-B, along with a platform to integrate other model checking
improvements via LTSmin in the future
An Object-Oriented Framework for Explicit-State Model Checking
This paper presents a conceptual architecture for an object-oriented framework to support the development of formal veriïŹcation tools (i.e. model checkers). The objective of the architecture is to support the reuse of algorithms and to encourage a modular design of tools. The conceptual framework is accompanied by a C++ implementation which provides reusable algorithms for the simulation and veriïŹcation of explicit-state models as well as a model representation for simple models based on guard-based process descriptions. The framework has been successfully used to develop a model checker for a subset of PROMELA
Symmetry Reduction Enables Model Checking of More Complex Emergent Behaviours of Swarm Navigation Algorithms
The emergent global behaviours of robotic swarms are important to achieve
their navigation task goals. These emergent behaviours can be verified to
assess their correctness, through techniques like model checking. Model
checking exhaustively explores all possible behaviours, based on a discrete
model of the system, such as a swarm in a grid. A common problem in model
checking is the state-space explosion that arises when the states of the model
are numerous. We propose a novel implementation of symmetry reduction, in the
form of encoding navigation algorithms relatively with respect to a reference,
based on the symmetrical properties of swarms in grids. We applied the relative
encoding to a swarm navigation algorithm, Alpha, modelled for the NuSMV model
checker. A comparison of the state-space and verification results with an
absolute (or global) and a relative encoding of the Alpha algorithm highlights
the advantages of our approach, allowing model checking larger grid sizes and
number of robots, and consequently, verifying more complex emergent behaviours.
For example, a property was verified for a grid with 3 robots and a maximum
allowed size of 8x8 cells in a global encoding, whereas this size was increased
to 16x16 using a relative encoding. Also, the time to verify a property for a
swarm of 3 robots in a 6x6 grid was reduced from almost 10 hours to only 7
minutes. Our approach is transferable to other swarm navigation algorithms.Comment: Accepted for presentation in Towards Autonomous Robotic Systems
(TAROS) 2015, Liverpool, U
Context-aware counter abstraction
The trend towards multi-core computing has made concurrent software an important target of computer-aided verification. Unfortunately, Model Checkers for such software suffer tremendously from combinatorial state space explosion. We show how to apply counter abstraction to real-world concurrent programs to factor out redundancy due to thread replication. The traditional global state representation as a vector of local states is replaced by a vector of thread counters, one per local state. In practice, straightforward implementations of this idea are unfavorably sensitive to the number of local states. We present a novel symbolic exploration algorithm that avoids this problem by carefully scheduling which counters to track at any moment during the search. We have carried out experiments on Boolean programs, an abstraction promoted by the success of the Slam project. The experiments give evidence of the applicability of our method to realistic programs, and of the often huge savings obtained in comparison to plain symbolic state space exploration, and to exploration optimized by partial-order methods. To our knowledge, our tool marks the first implementation of counter abstraction to programs with non-trivial local state spaces, resulting in a Model Checker for concurrent Boolean programs that promises true scalabilit
Graph- versus Vector-Based Analysis of a Consensus Protocol
The Paxos distributed consensus algorithm is a challenging case-study for
standard, vector-based model checking techniques. Due to asynchronous
communication, exhaustive analysis may generate very large state spaces already
for small model instances. In this paper, we show the advantages of graph
transformation as an alternative modelling technique. We model Paxos in a rich
declarative transformation language, featuring (among other things) nested
quantifiers, and we validate our model using the GROOVE model checker, a
graph-based tool that exploits isomorphism as a natural way to prune the state
space via symmetry reductions. We compare the results with those obtained by
the standard model checker Spin on the basis of a vector-based encoding of the
algorithm.Comment: In Proceedings GRAPHITE 2014, arXiv:1407.767
Automatic techniques for detecting and exploiting symmetry in model checking
The application of model checking is limited due to the state-space explosion problem â as the number of components represented by a model increase, the worst case size of the associated state-space grows exponentially. Current techniques can handle limited kinds of symmetry, e.g. full symmetry between identical components in a concurrent system. They avoid the problem of automatic symmetry detection by requiring the user to specify the presence of symmetry in a model (explicitly, or by annotating the associated specification using additional language keywords), or by restricting the input language of a model checker so that only symmetric systems can be specified. Additionally, computing unique representatives for each symmetric equivalence class is easy for these limited kinds of symmetry.
We present a theoretical framework for symmetry reduction which can be applied to explicit state model checking. The framework includes techniques for automatic symmetry detection using computational group theory, which can be applied with no additional user input. These techniques detect structural symmetries induced by the topology of a concurrent system, so our framework includes exact and approximate techniques to efficiently exploit arbitrary symmetry groups which may arise in this way. These techniques are also based on computational group theoretic methods.
We prove that our framework is logically sound, and demonstrate its general applicability to explicit state model checking. By providing a new symmetry reduction package for the SPIN model checker, we show that our framework can be feasibly implemented as part of a system which is widely used in both industry and academia. Through a study of SPIN users, we assess the usability of our automatic symmetry detection techniques in practice
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