Partial Order Reduction Techniques Research Articles

K∗ and Partial Order Reduction for Top-Quality Planning

Partial order reduction techniques are successfully used for various settings in planning, such as classical planning with A* search or with decoupled search, fully-observable non-deterministic planning with LAO*, planning with resources, or even goal recognition design. Here, we continue this trend and show that partial order reduction can be used for top-quality planning with K* search. We discuss the possible pitfalls of using stubborn sets for top-quality planning and the guarantees provided. We perform an empirical evaluation that shows the proposed approach to significantly improve over the current state of the art in unordered top-quality planning. The code is available at https://github.com/IBM/kstar.

Partial-order reduction for parity games and parameterised Boolean equation systems

In model checking, reduction techniques can be helpful tools to fight the state-space explosion problem. Partial-order reduction (POR) is a well-known example, and many POR variants have been developed over the years. However, none of these can be used in the context of model checking stutter-sensitive temporal properties. We propose POR techniques for parity games, a well-established formalism for solving a variety of decision problems, including model checking. As a result, we obtain the first POR method that is sound for the full modal upmu -calculus. We show how our technique can be applied to the fixed point logic called parameterised Boolean equation systems, which provides a high-level representation of parity games. Experiments with our implementation indicate that substantial reductions can be achieved.

Improving Online Railway Deadlock Detection using a Partial Order Reduction

Although railway dispatching on large national networks is gradually becoming more computerized, there are still major obstacles to retrofitting (semi-)autonomous control systems. In addition to requiring extensive and detailed digitalization of infrastructure models and information systems, exact optimization for railway dispatching is computationally hard. Heuristic algorithms and manual overrides are likely to be required for semi-autonomous railway operations for the foreseeable future. In this context, being able to detect problems such as deadlocks can be a valuable part of a runtime verification system. If bound-for-deadlock situations are correctly recognized as early as possible, human operators will have more time to better plan for recovery operations. Deadlock detection may also be useful for verification in a feedback loop with a heuristic or semi-autonomous dispatching algorithm if the dispatching algorithm cannot itself guarantee a deadlock-free plan. We describe a SAT-based planning algorithm for online detection of bound-for-deadlock situations. The algorithm exploits parallel updates of train positions and a partial order reduction technique to significantly reduce the number of state transitions (and correspondingly, the sizes of the formulas) in the SAT instances needed to prove whether a deadlock situation is bound to happen in the future. Implementation source code and benchmark instances are supplied, and a direct comparison against another recent study demonstrates significant performance gains.

Stubborn Sets Pruning for Privacy Preserving Planning

We adapt a partial order reduction technique based on stubborn sets to the setting of privacy-preserving multi-agent planning. We prove that the presented approach preserves optimality and show experimentally that it can significantly improve search performance on some domains.

On Improving Model Checking of Time Petri Nets and Its Application to the Formal Verification

Time Petri nets (TPN) are successfully used in the specification and analysis of distributed systems that involve explicit timing constraints. Especially, model checking TPN is a hopeful method for the formal verification of such complex systems. For this, it is promising to lean to the construction of an optimized version of the state space. The well-known methods of state space abstraction are SCG (state class graph) and ZBG (graph based on zones). For ZBG, a symbolic state represents the real evaluations of the clocks of the TPN; it is thus possible to directly check quantitative time properties. However, this method suffers from the state space explosion. To attenuate this problem, the authors propose in this paper to combine the ZBG approach with the partial order reduction technique based on stubborn set, leading thus to the proposal of a new state space abstraction called reduced zone-based graph (RZBG). The authors show via case studies the efficiency of the RZBG which is implemented and integrated within the 〖TPN-TCTL〗_h^∆ model checking in the model checker Romeo.

Parameterized Model Checking on the TSO Weak Memory Model

We present an extended version of the model checking modulo theories framework for verifying parameterized systems under the TSO weak memory model. Our extension relies on three main ingredients: (1) an axiomatic theory of the TSO memory model based on relations over (read, write) events, (2) a TSO-specific backward reachability algorithm and (3) an SMT solver for reasoning about TSO formulas. One of the main originality of our work is a partial order reduction technique that exploits specificities of the TSO memory model. We have implemented this framework in a new version of the Cubicle model checker called Cubicle- $$\mathscr {W}$$ . Our experiments show that Cubicle- $$\mathscr {W}$$ is expressive and efficient enough to automatically prove safety of concurrent algorithms, for an arbitrary number of processes, ranging from mutual exclusion to synchronization barriers translated from actual x86-TSO implementations.

RePOR: Mimicking humans on refactoring tasks. Are we there yet?

Refactoring is a maintenance activity that aims to improve design quality while preserving the behavior of a system. Several (semi)automated approaches have been proposed to support developers in this maintenance activity, based on the correction of anti-patterns, which are “poor” solutions to recurring design problems. However, little quantitative evidence exists about the impact of automatically refactored code on program comprehension, and in which context automated refactoring can be as effective as manual refactoring. Leveraging RePOR, an automated refactoring approach based on partial order reduction techniques, we performed an empirical study to investigate whether automated refactoring code structure affects the understandability of systems during comprehension tasks. (1) We surveyed 80 developers, asking them to identify from a set of 20 refactoring changes if they were generated by developers or by a tool, and to rate the refactoring changes according to their design quality; (2) we asked 30 developers to complete code comprehension tasks on 10 systems that were refactored by either a freelancer or an automated refactoring tool. To make comparison fair, for a subset of refactoring actions that introduce new code entities, only synthetic identifiers were presented to practitioners. We measured developers’ performance using the NASA task load index for their effort, the time that they spent performing the tasks, and their percentages of correct answers. Our findings, despite current technology limitations, show that it is reasonable to expect a refactoring tools to match developer code. Indeed, results show that for 3 out of the 5 anti-pattern types studied, developers could not recognize the origin of the refactoring (i.e., whether it was performed by a human or an automatic tool). We also observed that developers do not prefer human refactorings over automated refactorings, except when refactoring Blob classes; and that there is no statistically significant difference between the impact on code understandability of human refactorings and automated refactorings. We conclude that automated refactorings can be as effective as manual refactorings. However, for complex anti-patterns types like the Blob, the perceived quality achieved by developers is slightly higher.

Improving swarming using genetic algorithms

The verification of temporal properties against a given system may require the exploration of its full state space. In explicit model checking, this exploration uses a depth-first search and can be achieved with multiple randomized threads to increase performance. Nonetheless, the topology of the state space and the exploration order can cap the speedup up to a certain number of threads. This paper proposes a new technique that aims to tackle this limitation by generating artificial initial states, using genetic algorithms. Threads are then launched from these states and thus explore different parts of the state space. Our prototype implementation is 10% faster than state-of-the-art algorithms on a general benchmark and 40% on a specialized benchmark. Even if we expected a decrease in an order of magnitude, these results are still encouraging since they suggest a new way to handle existing limitations. Empirically, our technique seems well suited for “linear” topology, i.e., the one we can obtain when combining model checking algorithms with partial-order reduction techniques.

Optimal stateless model checking for reads-from equivalence under sequential consistency

We present a new approach for stateless model checking (SMC) of multithreaded programs under Sequential Consistency (SC) semantics. To combat state-space explosion, SMC is often equipped with a partial-order reduction technique, which defines an equivalence on executions, and only needs to explore one execution in each equivalence class. Recently, it has been observed that the commonly used equivalence of Mazurkiewicz traces can be coarsened but still cover all program crashes and assertion violations. However, for this coarser equivalence, which preserves only the reads-from relation from writes to reads, there is no SMC algorithm which is (i) optimal in the sense that it explores precisely one execution in each reads-from equivalence class, and (ii) efficient in the sense that it spends polynomial effort per class. We present the first SMC algorithm for SC that is both optimal and efficient in practice , meaning that it spends polynomial time per equivalence class on all programs that we have tried. This is achieved by a novel test that checks whether a given reads-from relation can arise in some execution. We have implemented the algorithm by extending Nidhugg, an SMC tool for C/C++ programs, with a new mode called rfsc. Our experimental results show that Nidhugg/rfsc, although slower than the fastest SMC tools in programs where tools happen to examine the same number of executions, always scales similarly or better than them, and outperforms them by an exponential factor in programs where the reads-from equivalence is coarser than the standard one. We also present two non-trivial use cases where the new equivalence is particularly effective, as well as the significant performance advantage that Nidhugg/rfsc offers compared to state-of-the-art SMC and systematic concurrency testing tools.

Value-centric dynamic partial order reduction

The verification of concurrent programs remains an open challenge, as thread interaction has to be accounted for, which leads to state-space explosion. Stateless model checking battles this problem by exploring traces rather than states of the program. As there are exponentially many traces, dynamic partial-order reduction (DPOR) techniques are used to partition the trace space into equivalence classes, and explore a few representatives from each class. The standard equivalence that underlies most DPOR techniques is the happens-before equivalence, however recent works have spawned a vivid interest towards coarser equivalences. The efficiency of such approaches is a product of two parameters: (i) the size of the partitioning induced by the equivalence, and (ii) the time spent by the exploration algorithm in each class of the partitioning. In this work, we present a new equivalence, called value-happens-before and show that it has two appealing features. First, value-happens-before is always at least as coarse as the happens-before equivalence, and can be even exponentially coarser. Second, the value-happens-before partitioning is efficiently explorable when the number of threads is bounded. We present an algorithm called value-centric DPOR ( VCDPOR ), which explores the underlying partitioning using polynomial time per class. Finally, we perform an experimental evaluation of VCDPOR on various benchmarks, and compare it against other state-of-the-art approaches. Our results show that value-happens-before typically induces a significant reduction in the size of the underlying partitioning, which leads to a considerable reduction in the running time for exploring the whole partitioning.

Effective lock handling in stateless model checking

Stateless Model Checking (SMC) is a verification technique for concurrent programs that checks for safety violations by exploring all possible thread interleavings. SMC is usually coupled with Partial Order Reduction (POR), which exploits the independence of instructions to avoid redundant explorations when an equivalent one has already been considered. While effective POR techniques have been developed for many different memory models, they are only able to exploit independence at the instruction level , which makes them unsuitable for programs with coarse-grained synchronization mechanisms such as locks . We present a lock-aware POR algorithm, LAPOR , that exploits independence at both instruction and critical section levels . This enables LAPOR to explore exponentially fewer interleavings than the state-of-the-art techniques for programs that use locks conservatively. Our algorithm is sound, complete, and optimal, and can be used for verifying programs under several different memory models. We implement LAPOR in a tool and show that it can be exponentially faster than the state-of-the-art model checkers.

Combining sequentialization-based verification of multi-threaded C programs with symbolic Partial Order Reduction

Sequentialization has been shown to be an effective symbolic verification technique for safety properties in multi-threaded C programs using POSIX threads. The tool Lazy-CSeq, which applies a lazy sequentialization scheme, demonstrated its efficiency by ranking top places within the concurrency division of the Competitions on Software Verification in recent years. This lazy sequentialization scheme encodes all thread schedules up to a given exploration bound into a single non-deterministic sequential C program. Another particularly effective technique to tackle the state explosion of multi-threaded programs is Partial Order Reduction (POR). It works by limiting the exploration of redundant thread execution orders (i.e., schedules) by exploiting independence. Integrating POR into lazy sequentialization can further significantly improve its scalability. However, a combination of both techniques can lead to unsoundness, i.e., reachability of states is not preserved within the exploration bound. The reason is that POR is not aware of the exploration bound; therefore, POR can prune a schedule which will reach a bug within the exploration bound and instead keep another (functionally) equivalent schedule which requires a larger exploration bound to reach the bug. This paper presents a novel implementation of lazy sequentialization, which integrates symbolic POR into the encoding to prune redundant schedules. An efficient pruning check is employed to make the POR technique aware of the exploration bound and thus avoid unsoundness, while still providing significant state space reductions. On the other hand, the integration of POR entails some additional encoding overhead that can also result in a performance slowdown. Such a case is avoided by a practical heuristic that only employs POR if the encoding overhead of POR is reasonable (i.e., less than 50%). Experimental evaluation shows that our proposed approach can provide considerable speed-ups.

Stubborn versus structural reductions for Petri nets

Partial order and structural reduction techniques are some of the most beneficial methods for state space reduction in reachability analysis of Petri nets. This is among others documented by the fact that these techniques are used by the leading tools in the annual Model Checking Contest (MCC) of Petri net tools. We suggest improved versions of a partial order reduction based on stubborn sets and of a structural reduction with additional new reduction rules, and we extend both methods for the application on Petri nets with weighted arcs and weighted inhibitor arcs. All algorithms are implemented in the open-source verification tool TAPAAL and evaluated on a large benchmark of Petri net models from MCC'17, including a comparison with the tool LoLA (the last year winner of the competition). The experiments document that both methods provide significant state space reductions and, even more importantly, that their combination is indeed beneficial as a further nontrivial state space reduction can be achieved.

Stackelberg Planning: Towards Effective Leader-Follower State Space Search

Inspired by work on Stackelberg security games, we introduce Stackelberg planning, where a leader player in a classical planning task chooses a minimum-cost action sequence aimed at maximizing the plan cost of a follower player in the same task. Such Stackelberg planning can provide useful analyses not only in planning-based security applications like network penetration testing, but also to measure robustness against perturbances in more traditional planning applications (e. g. with a leader sabotaging road network connections in transportation-type domains). To identify all equilibria---exhibiting the leader’s own-cost-vs.-follower-cost trade-off---we design leader-follower search, a state space search at the leader level which calls in each state an optimal planner at the follower level. We devise simple heuristic guidance, branch-and-bound style pruning, and partial-order reduction techniques for this setting. We run experiments on Stackelberg variants of IPC and pentesting benchmarks. In several domains, Stackelberg planning is quite feasible in practice.

Data-centric dynamic partial order reduction

We present a new dynamic partial-order reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partial-order reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes ( Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class. We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is control-centric, our new definition is data-centric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called data-centric DPOR, based on the observation equivalence. For acyclic architectures, our algorithm is guaranteed to explore exactly one representative trace from each observation class, while spending polynomial time per class. Hence, our algorithm is optimal wrt the observation equivalence, and in several cases explores exponentially fewer traces than any enumerative method based on the Mazurkiewicz equivalence. For cyclic architectures, we consider an equivalence between traces which is finer than the observation equivalence; but coarser than the Mazurkiewicz equivalence, and in some cases is exponentially coarser. Our data-centric DPOR algorithm remains optimal under this trace equivalence. Finally, we perform a basic experimental comparison between the existing Mazurkiewicz-based DPOR and our data-centric DPOR on a set of academic benchmarks. Our results show a significant reduction in both running time and the number of explored equivalence classes.

Delay-dependent partial order reduction technique for real time systems

Almost all partial order reduction techniques proposed for time Petri nets (TPNs in short) are based on the notion of Partially Ordered Sets. The idea is to explore simultaneously, by relaxing some firing order constraints of persistent transitions (An enabled transition is persistent, if it cannot be disabled until its firing.), several equivalent sequences, while computing the convex hull of the abstract states reached by these equivalent sequences. However, unlike timed automata, in the TPN state space abstractions, the union of the abstract states reached by different interleavings of the same set of non conflicting transitions is not necessarily identical to their convex hull. Moreover, the convex hull over-approximation preserves neither the boundedness nor the reachability properties of the TPN. In this context, the main challenge is to establish sufficient conditions over transitions that ensure, in addition to their persistency, identity between the union and the convex hull of the abstract states reachable by their different interleavings. This paper shows how to weaken the sufficient conditions proposed in the literature, by taking into better account the structure, the marking, the static and the dynamic time parameters of the TPN.

Precise slicing of interprocedural concurrent programs

Program slicing is an effective technique for analyzing concurrent programs. However, when a conventional closure-based slicing algorithmfor sequential programs is applied to a concurrent interprocedural program, the slice is usually imprecise owing to the intransitivity of interference dependence. Interference dependence arises when a statement uses a variable defined in another statement executed concurrently. In this study, we propose a global dependence analysis approach based on a program reachability graph, and construct a novel dependence graph calledmarking-statement dependence graph (MSDG), in which each vertex is a 2-tuple of program state and statement. In contrast to the conventional program dependence graph where the vertex is a statement, the dependence relation in MSDG is transitive. When traversing MSDG, a precise slice will be obtained. To enhance the slicing efficiency without loss of precision, our slicing algorithm adopts a hybrid strategy. The procedures containing interaction statements between threads are inlined and sliced by the slicing algorithm based on program reachability graphs while allowing other procedures to be sliced as sequential programs. We have implemented our algorithm and three other representative slicing algorithms, and conducted an empirical study on concurrent Java programs. The experimental results show that our algorithm computes more precise slices than the other algorithms. Using partial-order reduction techniques, which are effective for reducing the size of a program reachability graph without loss of precision, our algorithm is optimized, thereby improving its performance to some extent.

Stateless model checking of event-driven applications

Modern event-driven applications, such as, web pages and mobile apps, rely on asynchrony to ensure smooth end-user experience. Unfortunately, even though these applications are executed by a single event-loop thread, they can still exhibit nondeterministic behaviors depending on the execution order of interfering asynchronous events. As in classic shared-memory concurrency, this nondeterminism makes it challenging to discover errors that manifest only in specific schedules of events. In this work we propose the first stateless model checker for event-driven applications, called R4. Our algorithm systematically explores the nondeterminism in the application and concisely exposes its overall effect, which is useful for bug discovery. The algorithm builds on a combination of three key insights: (i) a dynamic partial order reduction (DPOR) technique for reducing the search space, tailored to the domain of event-driven applications, (ii) conflict-reversal bounding based on a hypothesis that most errors occur with a small number of event reorderings, and (iii) approximate replay of event sequences, which is critical for separating harmless from harmful nondeterminism. We instantiate R4 for the domain of client-side web applications and use it to analyze event interference in a number of real-world programs. The experimental results indicate that the precision and overall exploration capabilities of our system significantly exceed that of existing techniques.

Dynamic partial order reduction for relaxed memory models

Under a relaxed memory model such as TSO or PSO, a concurrent program running on a shared-memory multiprocessor may observe two types of nondeterminism: the nondeterminism in thread scheduling and the nondeterminism in store buffering. Although there is a large body of work on mitigating the scheduling nondeterminism during runtime verification, methods for soundly mitigating the store buffering nondeterminism are lacking. We propose a new dynamic partial order reduction (POR) algorithm for verifying concurrent programs under TSO and PSO. Our method relies on modeling both types of nondeterminism in a unified framework, which allows us to extend existing POR techniques to TSO and PSO without overhauling the verification algorithm. In addition to sound POR, we also propose a buffer-bounding method for more aggressively reducing the state space. We have implemented our new methods in a stateless model checking tool and demonstrated their effectiveness on a set of multithreaded C benchmarks.

Stubborn Sets for Time Petri Nets

The main limitation of the verification approaches based on state enumeration is the state explosion problem. The partial order reduction techniques aim at attenuating this problem by reducing the number of transitions to be fired from each state while preserving properties of interest. Among the reduction techniques proposed in the literature, this article considers the stubborn set method of Petri nets and investigates its extension to time Petri nets. It establishes some useful sufficient conditions for stubborn sets, which preserve deadlocks and k-boundedness of places.