Reachability Algorithm Research Articles

Formal Analysis of Drum-Boiler Units to Maximize the Load-Following Capabilities of Power Plants

The load-following capabilities of power plants became increasingly important in recent years as a means of ensuring a reliable operation of future power systems. In this work, we propose a generic approach, based on reachability analysis, to rigorously verify the safety of critical components that often pose limitations on the flexibility of conventional power plants to perform fast load changes. The proposed reachability algorithm makes it possible to compute the bounds of all possible trajectories for a range of operating conditions while simultaneously meeting the practical requirements of a real power plant. As an example, we consider the verification of the water level inside a drum unit. In contrast to previous work, our results are based on measurement data of a realistic configuration of a boiler system located within a 450 MW combined cycle plant in Germany. We use an abstract model which considers the modelling errors to ensure that all dynamic behaviors of the process are replicated by the abstraction. Through the implementation of our abstract model, we formally guarantee that the water level inside the drum always remains within safe limits for load changes equivalent to 40 MW which, as a result, exploits the power plant's adaptability and load-following capabilities.

A Symbolic SAT-Based Algorithm for Almost-Sure Reachability with Small Strategies in POMDPs

POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach.

A Fully Dynamic Reachability Algorithm for Directed Graphs with an Almost Linear Update Time

We obtain a new fully dynamic algorithm for the reachability problem in directed graphs. Our algorithm has an amortized update time of $O(m+n\log n)$ and a worst-case query time of $O(n)$, where $m$ is the current number of edges in the graph, and $n$ is the number of vertices in the graph. Each update operation either inserts a set of edges that touch the same vertex, or deletes an arbitrary set of edges. The algorithm is deterministic and uses fairly simple data structures. One of the ingredients used by this new algorithm may be interesting in its own right. It is a new dynamic algorithm for strong connectivity in directed graphs with an interesting ``retrospectiveness'' property. Each insert operation creates a new version of the graph. A delete operation deletes edges from all versions. Strong connectivity queries can be made on each version of the graph. The algorithm handles each update in $O(m\alpha(n))$ amortized time, and each query in $O(1)$ worst-case time, where $\alpha(n)$ is a functional in...

Efficient Geometric Operations on Convex Polyhedra, with an Application to Reachability Analysis of Hybrid Systems

We present a novel representation class for closed convex polyhedra, where a closed convex polyhedron is represented in terms of an orthogonal projection of a higher dimensional \(\mathcal{H}\)-polyhedron. The idea is to treat the pair of the projection and the polyhedron symbolically rather than to compute the actual described polyhedron. We call this representation a symbolic orthogonal projection, or a sop, for short. We show that fundamental geometrical operations, like affine transformations, intersections, Minkowski sums, and convex hulls, can be performed by simple block matrix operations on the representation. Due to the underlying \(\mathcal{H}\)-polyhedron, linear programs can be used to evaluate sops, e.g. the usage of template matrices easily yields tight over-approximations. Beyond this, we will also show how linear programming can be used to improve these over-approximations by adding additional supporting half-spaces, or even facet-defining half-spaces, to the over-approximation. On the other hand, we will also discuss some drawbacks of this representation, e.g. the lack of an efficient method to decide whether one sop is a subset of another sop, or the monotonic growth of the representation size under geometric operations. The second part deals with reachability analysis of hybrid systems with continuous dynamics described by linear differential inclusions and arbitrary affine maps for discrete updates. The invariants, guards, and sets of reachable states are given as convex polyhedra. First, we present a purely sop-based reachability algorithm where various geometric operations are performed exactly. Due to the monotonic growth of the representation size of the sops, this algorithm is not suited for practical applications. Then we propose a combination of the sop-based algorithm with a support function based reachability algorithm. Accompanied by some simple examples, we show that this combination results in an efficient reachability algorithm of better accuracy than pure support function based algorithm. We also discuss the current limitations of the proposed techniques and chart a path forward which might help us to solve linear programs over huge sops.

Verifying large modular systems using iterative abstraction refinement

Digital instrumentation and control (I&C) systems are increasingly used in the nuclear engineering domain. The exhaustive verification of these systems is challenging, and the usual verification methods such as testing and simulation are typically insufficient. Model checking is a formal method that is able to exhaustively analyse the behaviour of a model against a formally written specification. If the model checking tool detects a violation of the specification, it will give out a counter-example that demonstrates how the specification is violated in the system. Unfortunately, sometimes real life system designs are too big to be directly analysed by traditional model checking techniques. We have developed an iterative technique for model checking large modular systems. The technique uses abstraction based over-approximations of the model behaviour, combined with iterative refinement. The main contribution of the work is the concrete abstraction refinement technique based on the modular structure of the model, the dependency graph of the model, and a refinement sampling heuristic similar to delta debugging. The technique is geared towards proving properties, and outperforms BDD-based model checking, the k-induction technique, and the property directed reachability algorithm (PDR) in our experiments.

Automated preprocessing of environmental data

In this article we discuss automated preprocessing of environmental data for further use. Environmental data is by default heterogeneous, as it may consist of data from sources such as weather stations, weather radars, chemical sensors, acoustic sensors, and off-line laboratory analysis. When integrating data from such heterogeneous sources, it needs to be processed in a context dependent manner. In addition, there is no single generic processing method; rather, several atomic methods need to be applied and in an appropriate sequence. Furthermore, the problem is complicated by the requirements set by the intended use of the data. The requirements influence not only the set of applicable methods but also the application sequence. In this article, we study automation of the selection and sequencing of preprocessing methods based on the user requirements. As the main contribution, we propose here the use of characterizations and a reachability algorithm to solve the selection and sequencing problem. In this article, we present the algorithm and argue for its correctness. We also discuss, how the algorithm is implemented as a cloud service, and illustrate the use of the service with simple case studies.

Abductive Analysis of Administrative Policies in Rule-Based Access Control

In large organizations, access control policies are managed by multiple users (administrators). An administrative policy specifies how each user in an enterprise may change the policy. Fully understanding the consequences of an administrative policy in an enterprise system can be difficult, because of the scale and complexity of the access control policy and the administrative policy, and because sequences of changes by different users may interact in unexpected ways. Administrative policy analysis helps by answering questions such as user-permission reachability, which asks whether specified users can together change the policy in a way that achieves a specified goal, namely, granting a specified permission to a specified user. This paper presents a rule-based access control policy language, a rule-based administrative policy model that controls addition and removal of facts and rules, and an abductive analysis algorithm for user-permission reachability. Abductive analysis means that the algorithm can analyze policy rules even if the facts initially in the policy (e.g., information about users) are unavailable. The algorithm does this by computing minimal sets of facts that, if present in the initial policy, imply reachability of the goal.

Formal Synthesis of Control Policies for Continuous Time Markov Processes From Time-Bounded Temporal Logic Specifications

We consider the control synthesis problem for continuous-time Markov decision processes (CTMDPs), whose expected behaviors are measured by the satisfaction of Continuous Stochastic Logic (CSL) formulas. We present an extension of the CSL for CTMDPs involving sequential task specifications with continuous time constraints on the execution of those tasks. We then exploit model checking and time-bounded reachability algorithms to solve the CSL control synthesis problem. To illustrate the feasibility and effectiveness of our approach, we apply our methods to generate the optimal rate constants of a coupled set of biochemical reactions.

Approximated Symbolic Computations over Hybrid Automata

Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the real systems and infinite precision measurements. Such assumptions are not only unrealistic, but often lead to the construction of misleading models. For these reasons we believe that it is necessary to introduce more flexible semantics able to manage with noise, partial information, and finite precision instruments. In particular, in this paper we integrate in a single framework based on approximated semantics different over and under-approximation techniques for hybrid automata. Our framework allows to both compare, mix, and generalize such techniques obtaining different approximated reachability algorithms.

Multi-Core BDD Operations for Symbolic Reachability

This paper presents scalable parallel BDD operations for modern multi-core hardware. We aim at increasing the performance of reachability analysis in the context of model checking. Existing approaches focus on performing multiple independent BDD operations rather than parallelizing the BDD operations themselves. In the past, attempts at parallelizing BDD operations have been unsuccessful due to communication costs in shared memory.We solved this problem by extending an existing lockless hashtable to support BDDs and garbage collection and by implementing a lockless memoization table. Using these lockless hashtables and the work-stealing framework Wool, we implemented a multi-core BDD package called Sylvan.We provide the experimental results of using this multi-core BDD package in the framework of the model checker LTSmin. We measured the runtime of the reachability algorithm on several models from the BEEM model database on a 48-core machine, demonstrating speedups of over 30 for some models, which is a breakthrough compared to earlier work.In addition, we improved the standard symbolic reachability algorithm to use a modified BDD operation that calculates the relational product and the variable substitution in one step. We show that this new algorithm improves the performance of symbolic reachability and decreases the memory requirements by up to 40%.

An Improved Algorithm for Coverage Criteria Based Test Sequence Generation

In this paper, an improved reachability algorithm is presented to support automatic generation test suites for conformance testing. To select test cases, coverage criteria is specified formal structural criteria to be fulfilled by the test suite. The result is optimal in the sense that the set of test cases in the test suite which require the shortest possible accumulated time to cover the given coverage criterion. The key features of our technique are: (i) the coverage of given criteria is calculated in an on-the-fly manner, (ii) the sets of covered elements that arise during the analysis is efficiently manipulated, and (iii) requirement specification language is extended to express a variety of coverage criteria.

Optimal Management of Shuttle Robots in a High-Rise Warehouse Using Timed Automata Models

In warehousing systems, the speed of the removal and distribution of goods often represents a bottleneck as it limits the achievable throughput and, thus, the efficiency of the complete warehousing system. Consequently, an optimal management of the distribution of goods can lead to large efficiency and financial gains. In this contribution, it is shown for an accurate model of an industrial real-world high-rise warehouse (HRW), which is connected to a polymer production plant, that rigorous optimization of the distribution procedure can lead to a large efficiency increase in comparison to standard techniques. To this end, the distribution problem is modelled using timed automata (TA) in which the jobs arrive one after the other and are not known in advance. The TA-based approach, which was originally developed for standard scheduling problems, is extended to a reactive moving window approach that employs a cost-optimal reachability algorithm to compute optimal plans for the goods distribution. We show that compared to a typical first-come first-served dispatching rule, this approach can lead to throughput gains of more than 40%.

Controlling Polyvariance for Specialization-based Verification

Program specialization has been proposed as a means of improving constraint-based analysis of infinite state reactive systems. In particular, safety properties can be specified by constraint logic programs encoding backward or forward reachability algorithms. These programs are then transformed, before their use for checking safety, by specializing them with respect to the initial states in the case of backward reachability or with respect to the unsafe states in the case of forward reachability. By using the specialized reachability programs, we can considerably increase the number of successful verifications. An important feature of specialization algorithms is the so called polyvariance, that is, the number of specialized variants of the same predicate that are introduced by specialization. Depending on this feature, the specialization time, the size of the specialized program, and the number of successful verifications may vary. We present a specialization framework which is more general than previous proposals and provides control on polyvariance. We demonstrate, through experiments on several infinite state reactive systems, that by a careful choice of the degree of polyvariance we can design specialization-based verification procedures that are both efficient and precise.

Alternative specification and correctness proofs of the distributed network reachability algorithm DOI 10.5752/P.2316-9451.2012v1n1p5

The Distributed Network Reachability algorithm allows every node in a general topology network to determine which portions of the network are reachable and unreachable. The algorithm consists of three phases: test, dissemination, and reachability computation. During the testing phase each link is tested by one of the adjacent nodes at alternating testing intervals. Upon the detection of a new event, the tester starts the dissemination phase. In this work we both give an alternative specification of DNR that employs tokens at the testing phase allowing the pair of nodes connected by a link to share testing responsibilities, and give an alternative set of proofs for the algorithm.

A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets

Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net model and several translations to networks of timed automata have been proposed for this model. We present a direct, DBM-based algorithm for forward reachability analysis of bounded TAPNs extended with transport arcs, inhibitor arcs and age invariants. We also give a complete proof of its correctness, including reduction techniques based on symmetries and extrapolation. Finally, we augment the algorithm with a novel state-space reduction technique introducing a monotonic ordering on markings and prove its soundness even in the presence of monotonicity-breaking features like age invariants and inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and the experimental results document an encouraging performance compared to verification approaches that translate TAPN models to UPPAAL timed automata.

Time-Darts: A Data Structure for Verification of Closed Timed Automata

Symbolic data structures for model checking timed systems have been subject to a significant research, with Difference Bound Matrices (DBMs) still being the preferred data structure in several mature verification tools. In comparison, discretization offers an easy alternative, with all operations having linear-time complexity in the number of clocks, and yet valid for a large class of closed systems. Unfortunately, fine-grained discretization causes itself a state-space explosion. We introduce a new data structure called time-darts for the symbolic representation of state-spaces of timed automata. Compared with the complete discretization, a single time-dart allows to represent an arbitrary large set of states, yet the time complexity of operations on time-darts remain linear in the number of clocks. We prove the correctness of the suggested reachability algorithm and perform several experiments in order to compare the performance of time-darts and the complete discretization. The main conclusion is that in all our experiments the time-dart method outperforms the complete discretization and it scales significantly better for models with larger constants.

Distributed Diagnosis of Dynamic Events in Partitionable Arbitrary Topology Networks

This work introduces the Distributed Network Reachability (DNR) algorithm, a distributed system-level diagnosis algorithm that allows every node of a partitionable arbitrary topology network to determine which portions of the network are reachable and unreachable. DNR is the first distributed diagnosis algorithm that works in the presence of network partitions and healings caused by dynamic fault and repair events. Both crash and timing faults are assumed, and a faulty node is indistinguishable of a network partition. Every link is alternately tested by one of its adjacent nodes at subsequent testing intervals. Upon the detection of a new event, the new diagnostic information is disseminated to reachable nodes. New events can occur before the dissemination completes. Any time a new event is detected or informed, a working node may compute the network reachability using local diagnostic information. The bounded correctness of DNR is proved, including the bounded diagnostic latency, bounded startup and accuracy. Simulation results are presented for several random and regular topologies, showing the performance of the algorithm under highly dynamic fault situations.

Effective Batch Scheduling with Sequence-dependent Changeovers Using Reachability Analysis of Timed Automata Combined with Lower Bound Computations

Abstract In this contribution we discuss an extension of a recent approach to solve batch scheduling problems using reachability analysis for timed automata (TA) with embedded lower bound computations. We propose two bounding procedures embedded in the reachability algorithm to handle scheduling problems with sequence-dependent changeovers: (i) a MILP formulation (originally proposed by Manne 1960) extended with additional constraints to model setup and changeover operations and (ii) an improved minimum remaining processing time (MRPT) procedure. The efficiency of the proposed bounding procedures is evaluated on job shop problems with sequence-dependent changeovers. The comparative study shows that the MRPT-based bounding procedure is efficient and increases the overall performance significantly in comparison to the MILP-based bounding procedure.

Static Analysis of IMC

Process algebras formalism is highly suitable for producing succinct descriptions of reactive concurrent systems. Process algebras allow to represent them in a compositional way, as processes that run in parallel and interact, for example, through synchronisation or message passing. On the other hand, checking properties on process algebraic descriptions is often hard, while “unfolding” them into the Labelled Transition Systems can lead to the infamous state space explosion problem.In this work we use a subtype of Data Flow Analysis on systems defined by finite-state process algebras with CSP-type synchronisation – in particular, on our variant of IMC with a more permissive syntax, i.e. with a possibility to start a bounded number of new processes. We prove that the defined Pathway Analysis captures all the properties of the systems, i.e. is precise. The results of the Pathway Analysis can be therefore used as an intermediate representation format, which is more concise than the Labelled Transition System with all the states explicitly represented and more suitable for devising efficient verification algorithms of concurrent systems than their process algebraic descriptions – see, for example, the reachability algorithm in Skrypnyuk and Nielson (2011) [17].

Towards Symbolic Model-Based Mutation Testing: Combining Reachability and Refinement Checking

Model-based mutation testing uses altered test models to derive test cases that are able to reveal whether a modelled fault has been implemented. This requires conformance checking between the original and the mutated model. This paper presents an approach for symbolic conformance checking of action systems, which are well-suited to specify reactive systems. We also consider nondeterminism in our models. Hence, we do not check for equivalence, but for refinement. We encode the transition relation as well as the conformance relation as a constraint satisfaction problem and use a constraint solver in our reachability and refinement checking algorithms. Explicit conformance checking techniques often face state space explosion. First experimental evaluations show that our approach has potential to outperform explicit conformance checkers.