arXiv subjects

Javier Esparza

Publications and source records attributed to Javier Esparza.

At least 55 records · Page 3Linked to original sources

arXiv2019

Expressive Power of Broadcast Consensus Protocols

Population protocols are a formal model of computation by identical, anonymous mobile agents interacting in pairs. Their computational power is rather limited: Angluin et al. have shown that they can only compute the predicates over $\mathbb{N}^k$ expressible in Presburger arithmetic. For this reason, several extensions of the model have been proposed, including the addition of devices called cover-time services, absence detectors, and clocks. All these extensions increase the expressive power to the class of predicates over $\mathbb{N}^k$ lying in the complexity class NL when the input is given in unary. However, these devices are difficult to implement, since they require that an agent atomically receives messages from all other agents in a population of unknown size; moreover, the agent must know that they have all been received. Inspired by the work of the verification community on Emerson and Namjoshi's broadcast protocols, we show that NL-power is also achieved by extending population protocols with reliable broadcasts, a simpler, standard communication primitive.

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arXiv2019

Parameterized Analysis of Immediate Observation Petri Nets

We introduce immediate observation Petri nets, a class of interest in the study of population protocols (a model of distributed computation), and enzymatic chemical networks. In these areas, relevant analysis questions translate into parameterized Petri net problems: whether an infinite set of Petri nets with the same underlying net, but different initial markings, satisfy a given property. We study the parameterized reachability, coverability, and liveness problems for immediate observation Petri nets. We show that all three problems are in PSPACE for infinite sets of initial markings defined by counting constraints, a class sufficiently rich for the intended application. This is remarkable, since the problems are already PSPACE-hard when the set of markings is a singleton, i.e., in the non-parameterized case. We use these results to prove that the correctness problem for immediate observation population protocols is PSPACE-complete, answering a question left open in a previous paper.

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arXiv2019

Computing the Expected Execution Time of Probabilistic Workflow Nets

Free-Choice Workflow Petri nets, also known as Workflow Graphs, are a popular model in Business Process Modeling. In this paper we introduce Timed Probabilistic Workflow Nets (TPWNs), and give them a Markov Decision Process (MDP) semantics. Since the time needed to execute two parallel tasks is the maximum of the times, and not their sum, the expected time cannot be directly computed using the theory of MDPs with rewards. In our first contribution, we overcome this obstacle with the help of "earliest-first" schedulers, and give a single exponential-time algorithm for computing the expected time. In our second contribution, we show that computing the expected time is #P-hard, and so polynomial algorithms are very unlikely to exist. Further, #P-hardness holds even for workflows with a very simple structure in which all transitions times are 1 or 0, and all probabilities are 1 or 0.5. Our third and final contribution is an experimental investigation of the runtime of our algorithm on a set of industrial benchmarks. Despite the negative theoretical results, the results are very encouraging. In particular, the expected time of every workflow in a popular benchmark suite with 642 workflow nets can be computed in milliseconds.

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arXiv2018

Verification of Immediate Observation Population Protocols

Population protocols (Angluin et al., PODC, 2004) are a formal model of sensor networks consisting of identical mobile devices. Two devices can interact and thereby change their states. Computations are infinite sequences of interactions satisfying a strong fairness constraint. A population protocol is well-specified if for every initial configuration $C$ of devices, and every computation starting at $C$, all devices eventually agree on a consensus value depending only on $C$. If a protocol is well-specified, then it is said to compute the predicate that assigns to each initial configuration its consensus value. In a previous paper we have shown that the problem whether a given protocol is well-specified and the problem whether it computes a given predicate are decidable. However, in the same paper we prove that both problems are at least as hard as the reachability problem for Petri nets. Since all known algorithms for Petri net reachability have non-primitive recursive complexity, in this paper we restrict attention to immediate observation (IO) population protocols, a class introduced and studied in (Angluin et al., PODC, 2006). We show that both problems are solvable in exponential space for IO protocols. This is the first syntactically defined, interesting class of protocols for which an algorithm not requiring Petri net reachability is found.

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arXiv2018

Towards Efficient Verification of Population Protocols

Population protocols are a well established model of computation by anonymous, identical finite state agents. A protocol is well-specified if from every initial configuration, all fair executions reach a common consensus. The central verification question for population protocols is the well-specification problem: deciding if a given protocol is well-specified. Esparza et al. have recently shown that this problem is decidable, but with very high complexity: it is at least as hard as the Petri net reachability problem, which is EXPSPACE-hard, and for which only algorithms of non-primitive recursive complexity are currently known. In this paper we introduce the class WS3 of well-specified strongly-silent protocols and we prove that it is suitable for automatic verification. More precisely, we show that WS3 has the same computational power as general well-specified protocols, and captures standard protocols from the literature. Moreover, we show that the membership problem for WS3 reduces to solving boolean combinations of linear constraints over N. This allowed us to develop the first software able to automatically prove well-specification for all of the infinitely many possible inputs.

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arXiv2018

Automatic Analysis of Expected Termination Time for Population Protocols

Population protocols are a formal model of sensor networks consisting of identical mobile devices. Two devices can interact and thereby change their states. Computations are infinite sequences of interactions in which the interacting devices are chosen uniformly at random. In well designed population protocols, for every initial configuration of devices, and for every computation starting at this configuration, all devices eventually agree on a consensus value. We address the problem of automatically computing a parametric bound on the expected time the protocol needs to reach this consensus. We present the first algorithm that, when successful, outputs a function f(n) such that the expected time to consensus is bound by O(f(n)), where n is the number of devices executing the protocol. We experimentally show that our algorithm terminates and provides good bounds for many of the protocols found in the literature.

cs.LO↗

arXiv2018

One Theorem to Rule Them All: A Unified Translation of LTL into ω-Automata

We present a unified translation of LTL formulas into deterministic Rabin automata, limit-deterministic Büchi automata, and nondeterministic Büchi automata. The translations yield automata of asymptotically optimal size (double or single exponential, respectively). All three translations are derived from one single Master Theorem of purely logical nature. The Master Theorem decomposes the language of a formula into a positive boolean combination of languages that can be translated into ω-automata by elementary means. In particular, Safra's, ranking, and breakpoint constructions used in other translations are not needed.

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arXiv2018

Computing the concurrency threshold of sound free-choice workflow nets

Workflow graphs extend classical flow charts with concurrent fork and join nodes. They constitute the core of business processing languages such as BPMN or UML Activity Diagrams. The activities of a workflow graph are executed by humans or machines, generically called resources. If concurrent activities cannot be executed in parallel by lack of resources, the time needed to execute the workflow increases. We study the problem of computing the minimal number of resources necessary to fully exploit the concurrency of a given workflow, and execute it as fast as possible (i.e., as fast as with unlimited resources). We model this problem using free-choice Petri nets, which are known to be equivalent to workflow graphs. We analyze the computational complexity of two versions of the problem: computing the resource and concurrency thresholds. We use the results to design an algorithm to approximate the concurrency threshold, and evaluate it on a benchmark suite of 642 industrial examples. We show that it performs very well in practice: It always provides the exact value, and never takes more than 30 milliseconds for any workflow, even for those with a huge number of reachable markings.

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arXiv2018

Soundness in negotiations

Negotiations are a formalism for describing multiparty distributed cooperation. Alternatively, they can be seen as a model of concurrency with synchronized choice as communication primitive. Well-designed negotiations must be sound, meaning that, whatever its current state, the negotiation can still be completed. In earlier work, Esparza and Desel have shown that deciding soundness of a negotiation is Pspace-complete, and in Ptime if the negotiation is deterministic. They have also extended their polynomial soundness algorithm to an intermediate class of acyclic, non-deterministic negotiations. However, they did not analyze the runtime of the extended algorithm, and also left open the complexity of the soundness problem for the intermediate class. In the first part of this paper we revisit the soundness problem for deterministic negotiations, and show that it is Nlogspace-complete, improving on the earlier algorithm, which requires linear space. In the second part we answer the question left open by Esparza and Desel. We prove that the soundness problem can be solved in polynomial time for acyclic, weakly non- deterministic negotiations, a more general class than the one considered by them. In the third and final part, we show that the techniques developed in the first two parts of the paper can be applied to analysis problems other than soundness, including the problem of detecting race conditions, and several classical static analysis problems. More specifically, we show that, while these problems are intractable for arbitrary acyclic deterministic negotiations, they become tractable in the sound case. So soundness is not only a desirable behavioral property in itself, but also helps to analyze other properties.

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arXiv2018

Large Flocks of Small Birds: On the Minimal Size of Population Protocols

Population protocols are a well established model of distributed computation by mobile finite-state agents with very limited storage. A classical result establishes that population protocols compute exactly predicates definable in Presburger arithmetic. We initiate the study of the minimal amount of memory required to compute a given predicate as a function of its size. We present results on the predicates $x \geq n$ for $n \in \mathbb{N}$, and more generally on the predicates corresponding to systems of linear inequalities. We show that they can be computed by protocols with $O(\log n)$ states (or, more generally, logarithmic in the coefficients of the predicate), and that, surprisingly, some families of predicates can be computed by protocols with $O(\log\log n)$ states. We give essentially matching lower bounds for the class of 1-aware protocols.

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arXiv2017

Quantitative Implementation Strategies for Safety Controllers

We consider the symbolic controller synthesis approach to enforce safety specifications on perturbed, nonlinear control systems. In general, in each state of the system several control values might be applicable to enforce the safety requirement and in the implementation one has the burden of picking a particular control value out of possibly many. We present a class of implementation strategies to obtain a controller with certain performance guarantees. This class includes two existing implementation strategies from the literature, based on discounted payoff and mean-payoff games. We unify both approaches by using games characterized by a single discount factor determining the implementation. We evaluate different implementations from our class experimentally on two case studies. We show that the choice of the discount factor has a significant influence on the average long-term costs, and the best performance guarantee for the symbolic model does not result in the best implementation. Comparing the optimal choice of the discount factor here with the previously proposed values, the costs differ by a factor of up to 50. Our approach therefore yields a method to choose systematically a good implementation for safety controllers with quantitative objectives.

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arXiv2017

Static Analysis of Deterministic Negotiations

Negotiation diagrams are a model of concurrent computation akin to workflow Petri nets. Deterministic negotiation diagrams, equivalent to the much studied and used free-choice workflow Petri nets, are surprisingly amenable to verification. Soundness (a property close to deadlock-freedom) can be decided in PTIME. Further, other fundamental questions like computing summaries or the expected cost, can also be solved in PTIME for sound deterministic negotiation diagrams, while they are PSPACE-complete in the general case. In this paper we generalize and explain these results. We extend the classical "meet-over-all-paths" (MOP) formulation of static analysis problems to our concurrent setting, and introduce Mazurkiewicz-invariant analysis problems, which encompass the questions above and new ones. We show that any Mazurkiewicz-invariant analysis problem can be solved in PTIME for sound deterministic negotiations whenever it is in PTIME for sequential flow-graphs---even though the flow-graph of a deterministic negotiation diagram can be exponentially larger than the diagram itself. This gives a common explanation to the low-complexity of all the analysis questions studied so far. Finally, we show that classical gen/kill analyses are also an instance of our framework, and obtain a PTIME algorithm for detecting anti-patterns in free-choice workflow Petri nets. Our result is based on a novel decomposition theorem, of independent interest, showing that sound deterministic negotiation diagrams can be hierarchically decomposed into (possibly overlapping) smaller sound diagrams.

cs.LO↗

arXiv2017

From LTL and Limit-Deterministic Büchi Automata to Deterministic Parity Automata

Controller synthesis for general linear temporal logic (LTL) objectives is a challenging task. The standard approach involves translating the LTL objective into a deterministic parity automaton (DPA) by means of the Safra-Piterman construction. One of the challenges is the size of the DPA, which often grows very fast in practice, and can reach double exponential size in the length of the LTL formula. In this paper we describe a single exponential translation from limit-deterministic Büchi automata (LDBA) to DPA, and show that it can be concatenated with a recent efficient translation from LTL to LDBA to yield a double exponential, \enquote{Safraless} LTL-to-DPA construction. We also report on an implementation, a comparison with the SPOT library, and performance on several sets of formulas, including instances from the 2016 SyntComp competition.

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arXiv2016

On Negotiation as Concurrency Primitive II: Deterministic Cyclic Negotiations

We continue our study of negotations, a concurrency model with multiparty negotiation as primitive. In a previous paper (arXiv:13072145) we have provided a correct and complete set of reduction rules for sound, acyclic, and (weakly) deterministic negotiations. In this paper we extend this result to all deterministic negotiations, including cyclic ones. We also show that this set of rules allows one to decide soundness and to summarize negotiations in polynomial time.

cs.LO↗

arXiv2016

Negotiation as Concurrency Primitive

This paper introduces negotiations, a model of concurrency close to Petri nets, with multi-party negotiations as concurrency primitive. We study two fundamental analysis problems. The soundness problem consists in deciding if it is always possible for a negotiation to terminate successfully, whatever the current state is. Given a sound negotiation, the summarization problem aims at computing an equivalent one-step negotiation with the same input/output behavior. The soundness and summarization problems can be solved by means of simple algorithms acting on the state space of the negotiation, which however face the well-known state explosion problem. We study alternative algorithms that avoid the construction of the state space. In particular, we define reduction rules that simplify a negotiation while preserving the sound/non-sound character of the negotiation and its summary. In a first result we show that our rules are complete for the class of weakly deterministic acyclic negotiations, meaning that they reduce all sound negotiations in this class, and only them, to equivalent one-step negotiations. This provides algorithms for both the soundness and summarization problems that avoid the construction of the state space. We then study the class of deterministic negotiations. Our second main result shows that the rules are also complete for this class, even if the negotiation contains cycles. Moreover, we present an algorithm that completely reduces all sound deterministic negotiations, and only them, in polynomial time.

cs.LO↗

arXiv2016

Polynomial Analysis Algorithms for Free Choice Probabilistic Workflow Nets

We study Probabilistic Workflow Nets (PWNs), a model extending van der Aalst's workflow nets with probabilities. We give a semantics for PWNs in terms of Markov Decision Processes and introduce a reward model. Using a result by Varacca and Nielsen, we show that the expected reward of a complete execution of the PWN is independent of the scheduler. Extending previous work on reduction of non-probabilistic workflow nets, we present reduction rules that preserve the expected reward. The rules lead to a polynomial-time algorithm in the size of the PWN (not of the Markov decision process) for the computation of the expected reward. In contrast, since the Markov decision process of PWN can be exponentially larger than the PWN itself, all algorithms based on constructing the Markov decision process require exponential time. We report on a sample implementation and its performance on a collection of benchmarks.

cs.LO↗

arXiv2016

Reduction Rules for Colored Workflow Nets

We study Colored Workflow nets, a model based on Workflow nets enriched with data. Based on earlier work by Esparza and Desel[arXiv:1307.2145,arXiv:1403.4958] on the negotiation model of concurrency, we present reduction rules for our model. Contrary to previous work, our rules preserve not only soundness, but also the data flow semantics. For free choice nets, the rules reduce all sound nets (and only them) to a net with one single transition and the same data flow semantics. We give an explicit algorithm that requires only a polynomial number of rule applications.

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arXiv2015

Proceedings Sixth International Symposium on Games, Automata, Logics and Formal Verification

This volume contains the proceedings of the Sixth International Symposium on Games, Automata, Logic and Formal Verification (GandALF 2015). The symposium took place in Genoa, Italy, on the 21st and 22nd of September 2015. The proceedings of the symposium contain the abstracts of three invited talks and 13 papers that were accepted after a careful evaluation for presentation at the conference. The topics of the accepted papers cover algorithmic game theory, automata theory, formal verification, and modal and temporal logics.

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