Probabilistic Analysis of Wireless Systems Using Theorem Proving

J. Comput. Sci. Technol.

2010

Self Cite

Probabilistic techniques are widely used in the analysis of algorithms to estimate the computational complexity of algorithms or a computational problem. Traditionally, such analyses are performed using paper-and-pencil proofs and the results are sometimes validated using simulation techniques. These techniques are informal and thus may result in an inaccurate analysis. In this paper, we propose a formal technique for analyzing the expected time complexity of algorithms using higher-order-logic theorem proving. The approach calls for mathematically modeling the algorithm along with its inputs, using indicator random variables, in higher-order logic. This model is then used to formally reason about the expected time complexity of the underlying algorithm in a theorem prover. The paper includes the higher-order-logic formalization of indicator random variables, which are fundamental to the proposed infrastructure. In order to illustrate the practical effectiveness and utilization of the proposed infrastructure, the paper also includes the analysis of algorithms for three well-known problems, i.e., the hat-check problem, the birthday paradox and the hiring problem.

Section: Related Workmentioning

confidence: 99%

Formally Analyzing Expected Time Complexity of Algorithms Using Theorem Proving

J. Comput. Sci. Technol.

2010

Self Cite

“…Recently, the HOL probabilistic theorem proving framework has been greatly enriched so that it has been efficiently used to verify the stop-and-wait protocol [14], a stuck-at fault model for reconfigurable memory arrays [13] and the automated repeat request (ARQ) mechanism at the logic link control (LLC) layer of the General Packet Radio Service (GPRS) standard for Global System for Mobile Communications (GSM) [15]. In all these case studies, the authors illustrate the formal verification of some key statistical properties through the already formalized statistical quantities like the expectation and variance.…”

Section: Related Workmentioning

confidence: 99%

“…According to the probabilistic framework given in [15], we have to specify the higher-orderlogic functions describing the random components of the wireless system, and then verify the theorems which formalize the desired properties. In this section, we develop the HOL formalization of the coverage-based random scheduling algorithm for WSNs.…”

Section: Formalization Of the Coverage-based Randomized Scheduling Almentioning

confidence: 99%

Formal Analysis of a Scheduling Algorithm for Wireless Sensor Networks

Elleuch

Formal Methods and Software Engineering

et al. 2011

Self Cite

In wireless sensor networks (WSNs), scheduling of the sensors is considered to be the most effective energy conservation mechanism. The random and unpredictable deployment of sensors in many WSNs in the open fields makes the sensor scheduling problem very challenging and randomized scheduling algorithms are thus used. The performance of these algorithms is usually analyzed using simulation techniques, which do not offer 100% accurate results. In this paper, we overcome this limitation by using higher-order-logic theorem proving to formally analyze the coverage-based random scheduling; a variant of the random scheduling algorithm designed for wireless sensor networks. Particularly, we aim at formalizing this coverage-based random scheduling within the probabilistic framework developed in the HOL theorem prover. We also formally reason about the expected values of coverage intensity, the upper bound on the total number of disjoint subsets, given expected coverage intensity, the lower bound on the total number of nodes and the average detection delay inside the network.

“…Statistical properties of continuous random variables have been also verified in [10]. These foundations have been used to formally analyze various real-world applications including the Miller-Rabin primality test; a well-known and commercially used probabilistic algorithm [15], the stop-and-wait protocol [11], a stuck-at fault model for the reconfigurable memory arrays [13] and the automated repeat request (ARQ) mechanism at the logic link control (LLC) layer of the General Packet Radio Service (GPRS) standard for Global System for Mobile Communications (GSM) [12]. However, to the best of our knowledge, this is the first time that the probabilistic analysis using theorem proving technique is applied to analyze a forest fire detection WSN application in this paper.…”

Section: Related Workmentioning

confidence: 99%

Formal Probabilistic Analysis of a Wireless Sensor Network for Forest Fire Detection

Elleuch

Electron. Proc. Theor. Comput. Sci.

et al. 2013

Self Cite

Wireless Sensor Networks (WSNs) have been widely explored for forest fire detection, which is considered a fatal threat throughout the world. Energy conservation of sensor nodes is one of the biggest challenges in this context and random scheduling is frequently applied to overcome that. The performance analysis of these random scheduling approaches is traditionally done by paper-and-pencil proof methods or simulation. These traditional techniques cannot ascertain 100% accuracy, and thus are not suitable for analyzing a safety-critical application like forest fire detection using WSNs. In this paper, we propose to overcome this limitation by applying formal probabilistic analysis using theorem proving to verify scheduling performance of a real-world WSN for forest fire detection using a k-set randomized algorithm as an energy saving mechanism. In particular, we formally verify the expected values of coverage intensity, the upper bound on the total number of disjoint subsets, for a given coverage intensity, and the lower bound on the total number of nodes.