65,919 research outputs found

    Algebraic Watchdog: Mitigating Misbehavior in Wireless Network Coding

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    We propose a secure scheme for wireless network coding, called the algebraic watchdog. By enabling nodes to detect malicious behaviors probabilistically and use overheard messages to police their downstream neighbors locally, the algebraic watchdog delivers a secure global self-checking network. Unlike traditional Byzantine detection protocols which are receiver-based, this protocol gives the senders an active role in checking the node downstream. The key idea is inspired by Marti et al.'s watchdog-pathrater, which attempts to detect and mitigate the effects of routing misbehavior. As an initial building block of a such system, we first focus on a two-hop network. We present a graphical model to understand the inference process nodes execute to police their downstream neighbors; as well as to compute, analyze, and approximate the probabilities of misdetection and false detection. In addition, we present an algebraic analysis of the performance using an hypothesis testing framework that provides exact formulae for probabilities of false detection and misdetection. We then extend the algebraic watchdog to a more general network setting, and propose a protocol in which we can establish trust in coded systems in a distributed manner. We develop a graphical model to detect the presence of an adversarial node downstream within a general multi-hop network. The structure of the graphical model (a trellis) lends itself to well-known algorithms, such as the Viterbi algorithm, which can compute the probabilities of misdetection and false detection. We show analytically that as long as the min-cut is not dominated by the Byzantine adversaries, upstream nodes can monitor downstream neighbors and allow reliable communication with certain probability. Finally, we present simulation results that support our analysis.Comment: 10 pages, 10 figures, Submitted to IEEE Journal on Selected Areas in Communications (JSAC) "Advances in Military Networking and Communications

    Algebraic model checking for discrete linear dynamical systems

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    Model checking infinite-state systems is one of the central challenges in automated verification. In this survey we focus on an important and fundamental subclass of infinite-state systems, namely discrete linear dynamical systems. While such systems are ubiquitous in mathematics, physics, engineering, etc., in the present context our motivation stems from their relevance to the formal analysis and verification of program loops, weighted automata, hybrid systems, and control systems, amongst many others. Our main object of study is the problem of model checking temporal properties on the infinite orbit of a linear dynamical system, and our principal contribution is to show that for a rich class of properties this problem can be reduced to certain classical decision problems on linear recurrence sequences, notably the Skolem Problem. This leads us to discuss recent advances on the latter and to highlight the prospects for further progress on charting the algorithmic landscape of linear recurrence sequences and linear dynamical systems

    Algebraic Model Checking for Discrete Linear Dynamical Systems

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    Model checking infinite-state systems is one of the central challenges in automated verification. In this survey we focus on an important and fundamental subclass of infinite-state systems, namely discrete linear dynamical systems. While such systems are ubiquitous in mathematics, physics, engineering, etc., in the present context our motivation stems from their relevance to the formal analysis and verification of program loops, weighted automata, hybrid systems, and control systems, amongst many others. Our main object of study is the problem of model checking temporal properties on the infinite orbit of a linear dynamical system, and our principal contribution is to show that for a rich class of properties this problem can be reduced to certain classical decision problems on linear recurrence sequences, notably the Skolem Problem. This leads us to discuss recent advances on the latter and to highlight the prospects for further progress on charting the algorithmic landscape of linear recurrence sequences and linear dynamical systems

    ΠžΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΎΠ½Π½Ρ‹Π΅ ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Ρ‹ Π² Π°Ρ„Ρ„ΠΈΠ½Π½ΠΎΠΉ ΠΏΡ€ΠΎΠ²Π΅Ρ€ΠΊΠ΅ ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ

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    Symbolic model checking is based on a compact representation of sets of states and transition relations. At present there are three basic approaches of symbolic model checking: BDD-methods, bounded model checking using SAT-solvers, and various algebraic techniques, for example, constraint based model checking and regular model checking. In this paper we suggest improved algorithms for an algebraic data representation, namely, optimization algorithms for affine data structures.Бимвольная ΠΏΡ€ΠΎΠ²Π΅Ρ€ΠΊΠ° Π½Π° ΠΌΠΎΠ΄Π΅Π»ΠΈ основана Π½Π° ΠΊΠΎΠΌΠΏΠ°ΠΊΡ‚Π½ΠΎΠΌ прСдставлСнии мноТСств. На Π΄Π°Π½Π½Ρ‹ΠΉ ΠΌΠΎΠΌΠ΅Π½Ρ‚ Π΅ΡΡ‚ΡŒ Ρ‚Ρ€ΠΈ основных направлСния символьной ΠΏΡ€ΠΎΠ²Π΅Ρ€ΠΊΠΈ ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ: ΠΌΠ΅Ρ‚ΠΎΠ΄Ρ‹, основанныС Π½Π° Π±ΠΈΠ½Π°Ρ€Π½Ρ‹Ρ… Ρ€Π°Π·Ρ€Π΅ΡˆΠ°ΡŽΡ‰ΠΈΡ… Π΄ΠΈΠ°Π³Ρ€Π°ΠΌΠΌΠ°Ρ…, ограничСнная ΠΏΡ€ΠΎΠ²Π΅Ρ€ΠΊΠ° ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ, ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΡƒΡŽΡ‰Π°Ρ SAT-Ρ€Π΅ΡˆΠ°Ρ‚Π΅Π»ΠΈ, ΠΈ Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹Π΅ алгСбраичСскиС ΠΏΠΎΠ΄Ρ…ΠΎΠ΄Ρ‹ ΠΊ эффСктивному ΠΏΡ€Π΅Π΄ΡΡ‚Π°Π²Π»Π΅Π½ΠΈΡŽ Π΄Π°Π½Π½Ρ‹Ρ…. Π’ Π΄Π°Π½Π½ΠΎΠΉ Ρ€Π°Π±ΠΎΡ‚Π΅ прСдлагаСтся Ρ€Π°ΡΡΠΌΠΎΡ‚Ρ€Π΅Ρ‚ΡŒ ΡƒΠ»ΡƒΡ‡ΡˆΠ΅Π½Π½Ρ‹Π΅ Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΡ‹ манипуляции с алгСбраичСским прСдставлСниСм Π΄Π°Π½Π½Ρ‹Ρ…, Π° ΠΈΠΌΠ΅Π½Π½ΠΎ Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΡ‹ ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΈ Π°Ρ„Ρ„ΠΈΠ½Π½Ρ‹Ρ… прСдставлСний Π΄Π°Π½Π½Ρ‹Ρ…

    A balancing act : analyzing a distributed lift system

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    The process-algebraic language Β΅crl is used to analyze an existing distributed system for lifting trucks. Four errors were found in the original design. We propose solutions for these problems and show by means of model-checking that the modified system meets the requirements
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