Separation of Circulating Tokens

Self-stabilizing distributed control is often modeled by token abstractions. A system with a single token may implement mutual exclusion; a system with multiple tokens may ensure that immediate neighbors do not simultaneously enjoy a privilege. For a cyber-physical system, tokens may represent physical objects whose movement is controlled. The problem studied in this paper is to ensure that a synchronous system with m circulating tokens has at least d distance between tokens. This problem is first considered in a ring where d is given whilst m and the ring size n are unknown. The protocol solving this problem can be uniform, with all processes running the same program, or it can be non-uniform, with some processes acting only as token relays. The protocol for this first problem is simple, and can be expressed with Petri net formalism. A second problem is to maximize d when m is given, and n is unknown. For the second problem, the paper presents a non-uniform protocol with a single corrective process.Comment: 22 pages, 7 figures, epsf and pstricks in LaTe

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.Comment: 29 pages, 1 figur

Dagstuhl News January - December 2000

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic

Structural Invariants for the Verification of Systems with Parameterized Architectures

We consider parameterized concurrent systems consisting of a finite but unknown number of components, obtained by replicating a given set of finite state automata. Components communicate by executing atomic interactions whose participants update their states simultaneously. We introduce an interaction logic to specify both the type of interactions (e.g.\ rendez-vous, broadcast) and the topology of the system (e.g.\ pipeline, ring). The logic can be easily embedded in monadic second order logic of finitely many successors, and is therefore decidable. Proving safety properties of such a parameterized system, like deadlock freedom or mutual exclusion, requires to infer an inductive invariant that contains all reachable states of all system instances, and no unsafe state. We present a method to automatically synthesize inductive invariants directly from the formula describing the interactions, without costly fixed point iterations. We experimentally prove that this invariant is strong enough to verify safety properties of a large number of systems including textbook examples (dining philosophers, synchronization schemes), classical mutual exclusion algorithms, cache-coherence protocols and self-stabilization algorithms, for an arbitrary number of components.Comment: preprint; to be published in the proceedings of TACAS2

Measurements, Models, Systems and Design

531 s.

Hardness of Computing and Approximating Predicates and Functions with Leaderless Population Protocols

Population protocols are a distributed computing model appropriate for describing massive numbers of agents with very limited computational power (finite automata in this paper), such as sensor networks or programmable chemical reaction networks in synthetic biology. A population protocol is said to require a leader if every valid initial configuration contains a single agent in a special "leader" state that helps to coordinate the computation. Although the class of predicates and functions computable with probability 1 (stable computation) is the same whether a leader is required or not (semilinear functions and predicates), it is not known whether a leader is necessary for fast computation. Due to the large number of agents n (synthetic molecular systems routinely have trillions of molecules), efficient population protocols are generally defined as those computing in polylogarithmic in n (parallel) time. We consider population protocols that start in leaderless initial configurations, and the computation is regarded finished when the population protocol reaches a configuration from which a different output is no longer reachable. In this setting we show that a wide class of functions and predicates computable by population protocols are not efficiently computable (they require at least linear time), nor are some linear functions even efficiently approximable. It requires at least linear time for a population protocol even to approximate division by a constant or subtraction (or any linear function with a coefficient outside of N), in the sense that for sufficiently small gamma > 0, the output of a sublinear time protocol can stabilize outside the interval f(m) (1 +/- gamma) on infinitely many inputs m. In a complementary positive result, we show that with a sufficiently large value of gamma, a population protocol can approximate any linear f with nonnegative rational coefficients, within approximation factor gamma, in O(log n) time. We also show that it requires linear time to exactly compute a wide range of semilinear functions (e.g., f(m)=m if m is even and 2m if m is odd) and predicates (e.g., parity, equality)

Guidelines for Verification of Population Protocols

We address the problem of verification by model-checking of the basic population protocol (\pp) model of Angluin et al. This problem has received special attention the last two years and new tools have been proposed to deal with it. We show that the problem can be solved using the existing model-checking tools, e.g., Spin and Prism. For this, we apply the counting abstraction to obtain an abstract model of a \pp\ which can be efficiently verified by the existing model-checking tools. Moreover, this abstraction preserves the correct stabilization property of \pp. To deal with the fairness assumed in the \pp\ model, we provide two recipes. The first one gives sufficient conditions under which the \pp\ fairness can be replaced by the weak fairness implemented in Spin. We show that this recipe can be applied to several \pp\ models. In the second recipe, we show how to use the probabilistic model-checking and the tool Prism to deal completely with the fairness of the \pp\ model. The correctness of this recipe is based on existing theorems on finite discrete Markov chains

Stable Leader Election in Population Protocols Requires Linear Time

A population protocol *stably elects a leader* if, for all $n$, starting from an initial configuration with $n$ agents each in an identical state, with probability 1 it reaches a configuration $\mathbf{y}$ that is correct (exactly one agent is in a special leader state $\ell$) and stable (every configuration reachable from $\mathbf{y}$ also has a single agent in state $\ell$). We show that any population protocol that stably elects a leader requires $\Omega(n)$ expected "parallel time" --- $\Omega(n^2)$ expected total pairwise interactions --- to reach such a stable configuration. Our result also informs the understanding of the time complexity of chemical self-organization by showing an essential difficulty in generating exact quantities of molecular species quickly.Comment: accepted to Distributed Computing special issue of invited papers from DISC 2015; significantly revised proof structure and intuitive explanation

A Neural Radiance Field-Based Architecture for Intelligent Multilayered View Synthesis

A mobile ad hoc network is made up of a number of wireless portable nodes that spontaneously come together en route for establish a transitory network with no need for any central management. A mobile ad hoc network (MANET) is made up of a sizable and reasonably dense community of mobile nodes that travel across any terrain and rely solely on wireless interfaces for communication, not on any well before centralized management. Furthermore, routing be supposed to offer a method for instantly delivering data across a network between any two nodes. Finding the best packet routing from across infrastructure is the major issue, though. The proposed protocol's major goal is to identify the least-expensive nominal capacity acquisition that assures the transportation of realistic transport that ensures its durability in the event of any node failure. This study suggests the Optimized Route Selection via Red Imported Fire Ants (RIFA) Strategy as a way to improve on-demand source routing systems. Predicting Route Failure and energy Utilization is used to pick the path during the routing phase. Proposed work assess the results of the comparisons based on performance parameters like as energy usage, packet delivery rate (PDR), and end-to-end (E2E) delay. The outcome demonstrates that the proposed strategy is preferable and increases network lifetime while lowering node energy consumption and typical E2E delay under the majority of network performance measures and factors