scholarly journals Towards efficient verification of population protocols

2021 ◽  
Author(s):  
Michael Blondin ◽  
Javier Esparza ◽  
Stefan Jaax ◽  
Philipp J. Meyer
Keyword(s):  
Linear Constraints ◽  
Computational Power ◽  
High Complexity ◽  
Reachability Problem ◽  
Population Protocols ◽  
Finite State ◽  
State Agents ◽  
Efficient Verification ◽  
Primitive Recursive ◽  
Very High

AbstractPopulation 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 of the protocol 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 -hard, and for which only algorithms of non-primitive recursive complexity are currently known. In this paper we introduce the class $${ WS}^3$$ WS 3 of well-specified strongly-silent protocols and we prove that it is suitable for automatic verification. More precisely, we show that $${ WS}^3$$ WS 3 has the same computational power as general well-specified protocols, and captures standard protocols from the literature. Moreover, we show that the membership and correctness problems for $${ WS}^3$$ WS 3 reduce to solving boolean combinations of linear constraints over $${\mathbb {N}}$$ N . This allowed us to develop the first software able to automatically prove correctness for all of the infinitely many possible inputs.

scholarly journals The complexity of verifying population protocols

2021 ◽  
Vol 34 (2) ◽  
pp. 133-177
Author(s):  
Javier Esparza ◽  
Stefan Jaax ◽  
Mikhail Raskin ◽  
Chana Weil-Kennedy
Keyword(s):  
Expressive Power ◽  
Property A ◽  
Reachability Problem ◽  
Seminal Paper ◽  
Population Protocols ◽  
Finite State ◽  
State Agents ◽  
Exhaustive Study ◽  
Main Model ◽  
Main Population

AbstractPopulation protocols (Angluin et al. in PODC, 2004) are a model of distributed computation in which indistinguishable, finite-state agents interact in pairs to decide if their initial configuration, i.e., the initial number of agents in each state, satisfies a given property. In a seminal paper Angluin et al. classified population protocols according to their communication mechanism, and conducted an exhaustive study of the expressive power of each class, that is, of the properties they can decide (Angluin et al. in Distrib Comput 20(4):279–304, 2007). In this paper we study the correctness problem for population protocols, i.e., whether a given protocol decides a given property. A previous paper (Esparza et al. in Acta Inform 54(2):191–215, 2017) has shown that the problem is decidable for the main population protocol model, but at least as hard as the reachability problem for Petri nets, which has recently been proved to have non-elementary complexity. Motivated by this result, we study the computational complexity of the correctness problem for all other classes introduced by Angluin et al., some of which are less powerful than the main model. Our main results show that for the class of observation models the complexity of the problem is much lower, ranging from $$\varPi _2^p$$ Π 2 p to .

scholarly journals Finding Cut-Offs in Leaderless Rendez-Vous Protocols is Easy

2021 ◽  
pp. 42-61
Author(s):  
A. R. Balasubramanian ◽  
Javier Esparza ◽  
Mikhail Raskin
Keyword(s):  
Lower Bounds ◽  
Petri Net ◽  
Special Class ◽  
Upper Bounds ◽  
Initial State ◽  
Reachability Problem ◽  
Final State ◽  
Final Configuration ◽  
Finite State ◽  
State Agents

AbstractIn rendez-vous protocols an arbitrarily large number of indistinguishable finite-state agents interact in pairs. The cut-off problem asks if there exists a number B such that all initial configurations of the protocol with at least B agents in a given initial state can reach a final configuration with all agents in a given final state. In a recent paper [17], Horn and Sangnier prove that the cut-off problem is equivalent to the Petri net reachability problem for protocols with a leader, and in "Image missing" for leaderless protocols. Further, for the special class of symmetric protocols they reduce these bounds to "Image missing" and "Image missing" , respectively. The problem of lowering these upper bounds or finding matching lower bounds is left open. We show that the cut-off problem is "Image missing" -complete for leaderless protocols, "Image missing" -complete for symmetric protocols with a leader, and in "Image missing" for leaderless symmetric protocols, thereby solving all the problems left open in [17].

scholarly journals The Decidability of Verification under PS 2.0

2021 ◽  
pp. 1-29
Author(s):  
Parosh Aziz Abdulla ◽  
Mohamed Faouzi Atig ◽  
Adwait Godbole ◽  
S. Krishna ◽  
Viktor Vafeiadis
Keyword(s):  
Global Memory ◽  
Program Transformations ◽  
Reachability Problem ◽  
Context Switching ◽  
Input Program ◽  
Finite State ◽  
Memory Accesses ◽  
Primitive Recursive

AbstractWe consider the reachability problem for finite-state multi-threaded programs under thepromising semantics() of Lee et al., which captures most common program transformations. Since reachability is already known to be undecidable in the fragment of with only release-acquire accesses (-), we consider the fragment with only relaxed accesses and promises (). We show that reachability under is undecidable in general and that it becomes decidable, albeit non-primitive recursive, if we bound the number of promises.Given these results, we consider a bounded version of the reachability problem. To this end, we bound both the number of promises and of “view-switches”, i.e., the number of times the processes may switch their local views of the global memory. We provide a code-to-code translation from an input program under (with relaxed and release-acquire memory accesses along with promises) to a program under SC, thereby reducing the bounded reachability problem under to the bounded context-switching problem under SC. We have implemented a tool and tested it on a set of benchmarks, demonstrating that typical bugs in programs can be found with a small bound.

scholarly journals Running Time Analysis of Broadcast Consensus Protocols

2021 ◽  
pp. 164-183
Author(s):  
Philipp Czerner ◽  
Stefan Jaax
Keyword(s):  
Turing Machine ◽  
Polynomial Time ◽  
Execution Time ◽  
Time Analysis ◽  
Asymptotically Optimal ◽  
Population Protocols ◽  
Running Time ◽  
Running Time Analysis ◽  
Finite State ◽  
State Agents

AbstractBroadcast consensus protocols (BCPs) are a model of computation, in which anonymous, identical, finite-state agents compute by sending/receiving global broadcasts. BCPs are known to compute all number predicates in $$\mathsf {NL}=\mathsf {NSPACE}(\log n)$$ NL = NSPACE ( log n ) where n is the number of agents. They can be considered an extension of the well-established model of population protocols. This paper investigates execution time characteristics of BCPs. We show that every predicate computable by population protocols is computable by a BCP with expected $$\mathcal {O}(n \log n)$$ O ( n log n ) interactions, which is asymptotically optimal. We further show that every log-space, randomized Turing machine can be simulated by a BCP with $$\mathcal {O}(n \log n \cdot T)$$ O ( n log n · T ) interactions in expectation, where T is the expected runtime of the Turing machine. This allows us to characterise polynomial-time BCPs as computing exactly the number predicates in $$\mathsf {ZPL}$$ ZPL , i.e. predicates decidable by log-space, randomised Turing machine with zero-error in expected polynomial time where the input is encoded as unary.

Stable Encoding of Finite-State Machines in Discrete-Time Recurrent Neural Nets with Sigmoid Units

2000 ◽  
Vol 12 (9) ◽  
pp. 2129-2174 ◽  
Author(s):  
Rafael C. Carrasco ◽  
Mikel L. Forcada ◽  
M. Ángeles Valdés-Muñoz ◽  
Ramón P. Ñeco
Keyword(s):  
Discrete Time ◽  
Finite State Machine ◽  
Finite State Machines ◽  
Activation Function ◽  
Neural Nets ◽  
State Machines ◽  
Computational Power ◽  
Simple Strategy ◽  
Finite State ◽  
Detailed Presentation

There has been a lot of interest in the use of discrete-time recurrent neural nets (DTRNN) to learn finite-state tasks, with interesting results regarding the induction of simple finite-state machines from input–output strings. Parallel work has studied the computational power of DTRNN in connection with finite-state computation. This article describes a simple strategy to devise stable encodings of finite-state machines in computationally capable discrete-time recurrent neural architectures with sigmoid units and gives a detailed presentation on how this strategy may be applied to encode a general class of finite-state machines in a variety of commonly used first- and second-order recurrent neural networks. Unlike previous work that either imposed some restrictions to state values or used a detailed analysis based on fixed-point attractors, our approach applies to any positive, bounded, strictly growing, continuous activation function and uses simple bounding criteria based on a study of the conditions under which a proposed encoding scheme guarantees that the DTRNN is actually behaving as a finite-state machine.

SOME COMPLEXITY RESULTS FOR RINGS OF PETRI NETS

1994 ◽  
Vol 05 (03n04) ◽  
pp. 281-292
Author(s):  
HSU-CHUN YEN ◽  
BOW-YAW WANG ◽  
MING-SHANG YANG
Keyword(s):  
Petri Nets ◽  
State Machines ◽  
Slight Improvement ◽  
Reachability Problem ◽  
Encoding Scheme ◽  
N Cycle ◽  
Vector Addition ◽  
Finite State ◽  
Boundedness Problem ◽  
Compare And Contrast

We define a subclass of Petri nets called m–state n–cycle Petri nets, each of which can be thought of as a ring of n bounded (by m states) Petri nets using n potentially unbounded places as joins. Let Ring(n, l, m) be the class of m–state n–cycle Petri nets in which the largest integer mentioned can be represented in l bits (when the standard binary encoding scheme is used). As it turns out, both the reachability problem and the boundedness problem can be decided in O(n(l+log m)) nondeterministic space. Our results provide a slight improvement over previous results for the so-called cyclic communicating finite state machines. We also compare and contrast our results with that of VASS(n, l, s), which represents the class of n-dimensional s-state vector addition systems with states where the largest integer mentioned can be described in l bits.

scholarly journals PROPOSE SAFETY ENGINEERING CONCEPT SPEED LIMITER AND FATIGUE CONTROL USING SLIFA FOR TRUCK AND BUS

SINERGI ◽  
2020 ◽  
Vol 24 (3) ◽  
pp. 237
Author(s):  
Hadi Pranoto ◽  
Andi Adriansyah ◽  
Dafit Feriyanto ◽  
Abdi Wahab ◽  
Supaat Zakaria
Keyword(s):  
Fuel Consumption ◽  
Traffic Accidents ◽  
Performance Tests ◽  
Safety Engineering ◽  
High Complexity ◽  
Safety Device ◽  
Severe Problem ◽  
Complexity Problem ◽  
Very High ◽  
Engineering Concept

In 2015, there were 55 deaths from 6,231 accident cases that occurred in Jakarta. A severe problem in Indonesia is the absence of a unique safety device in both commercial transport or personal vehicles and the very high complexity problem of human highways. Consequently, there are many traffic accidents caused by the negligence of the driver, such as driving a vehicle in a drunken, tired, drowsy, or over-limit speed. Therefore, it needs to be innovative using devices to increase speed but able to detect the level of tired or sleepy drivers. This paper tries to propose a concept of improving safety engineering by developing devices that can control the speed and level of safety of trucks and buses, named SLIFA. The proposed device captures the driver's condition by looking at the eyes, size of mouth evaporating, and heart rate conditions.  Theses condition will be measured with a particular scale to determine the fatigue level of the driver. Some performance tests have been carried out on truck and bus with 122 Nm and 112 Nm torque wheels and 339 HP and 329 HP power values, respectively, and the minimum speed is 62 km/h. At a top speed of 70 km / h, the torque and power of the truck are 135Nm and 370HP, with average fuel consumption of 3.43 liters/km before SLIFA installation and average fuel consumption of 4.2 liters/km after SLIFA installation. SLIFA can be said to have functional eligibility and can cut fuel consumption by 81 percent.

scholarly journals Analytical model for estimating the production and composition of gas resulted through gasification

2021 ◽  
Vol 286 ◽  
pp. 01011
Author(s):  
Lucian Mihăescu ◽  
Ionel Pîșă ◽  
Iulia Simion ◽  
Gabriel Paul Negreanu
Keyword(s):  
Functional Results ◽  
Air Distribution ◽  
Fuel Composition ◽  
High Complexity ◽  
Preliminary Calculation ◽  
Concurrent Flow ◽  
Complex Calculation ◽  
Process Behavior ◽  
Very High ◽  
Calculation Models

For the modelling of gasification processes, several models have been developed over the years. It is remarked that gasification calculation models of very high complexity entail some complications. Therefore, simpler mathematical representations of gasification characteristics and process behavior are required as a first step in addressing such systems. The preliminary calculation simplicity is needed form two perspectives: First – the pre-sizing of gasification installations, and second – the estimation of experimental or functional results. For this kind of topics, an adequate simplified model should be defined. Further, to validate the results it will be necessary to use complex calculation models. The model proposed in this paper addresses gasification with distributive air in the air distribution current, considering general concurrent flow of air fuel. Previous successful investigations, conducted by the present research team, are taken into account within model definition stages. Thus, the work presented here provides useful advances in the field of mathematical modeling of gasification processes. The originality of the model consists in its easy computational accessibility, which allows the approach of technological optimizations, such as the variation of excess air and fuel composition.

Flows at Moderate Reynolds Numbers

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Steady State ◽  
Reynolds Numbers ◽  
Complex Geometries ◽  
Computational Power ◽  
Flow Configuration ◽  
Major Interest ◽  
Long Time ◽  
Pulsatile Flows ◽  
Short Time ◽  
Very High

This chapter presents the application of LBE to flows at moderate Reynolds numbers, typically hundreds to thousands. This is an important area of theoretical and applied fluid mechanics, one that relates, for instance, to the onset of nonlinear instabilities and their effects on the transport properties of the unsteady flow configuration. The regime of Reynolds numbers at which these instabilities take place is usually not very high, of the order of thousands, hence basically within reach of present day computer capabilities. Nonetheless, following the full evolution of these transitional flows requires very long-time integrations with short time-steps, which command substantial computational power. Therefore, efficient numerical methods are in great demand. Also of major interest are steady-state or pulsatile flows at moderate Reynolds numbers in complex geometries, such as they occur, for instance, in hemodynamic applications. The application of LBE to such flows will also briefly be mentioned

Lack of Naturalness in Human-Computer Interactions

2017 ◽  
pp. 9-46
Keyword(s):  
Real Time ◽  
Human Computer Interactions ◽  
High Complexity ◽  
Time Work ◽  
State Of Affairs ◽  
Natural Interactions ◽  
Very High ◽  
Computer Environments ◽  
Software Intensive ◽  
Computer Interactions

There is a problematic difference between interactions of a human with natural and computer environments. The negatives of this difference are particularly painful in the design of software intensive systems, the success of which is unpredictable and extremely low. The root reason for such state of affairs is a very high complexity with which the designers have deals. What we name as “Complexity” is a characteristic of estimations that is discovered in interactions of a human or humans with perceived essences. Therefore, for example, designers need means that will help them in interactions with environments of their activity during real-time work. This chapter tries to show that one of the possible directions of mastering the complexity is bound with the possibility for designers to create conditions of interactions that are similar to conditions of natural interactions. In this case, both types of interactions will be intertwined in coordination in search of simplifying an arisen complexity.

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