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211
Principles and methods of Testing Finite State Machines  a survey
 PROCEEDINGS OF IEEE
, 1996
"... With advanced computer technology, systems are getting larger to fulfill more complicated tasks, however, they are also becoming less reliable. Consequently, testing is an indispensable part of system design and implementation; yet it has proved to be a formidable task for complex systems. This moti ..."
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Cited by 339 (14 self)
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With advanced computer technology, systems are getting larger to fulfill more complicated tasks, however, they are also becoming less reliable. Consequently, testing is an indispensable part of system design and implementation; yet it has proved to be a formidable task for complex systems. This motivates the study of testing finite state machines to ensure the correct functioning of systems and to discover aspects of their behavior. A finite state machine contains a finite number of states and produces outputs on state transitions after receiving inputs. Finite state machines are widely used to model systems in diverse areas, including sequential circuits, certain types of programs, and, more recently, communication protocols. In a testing problem we have a machine about which we lack some information; we would like to deduce this information by providing a sequence of inputs to the machine and observing the outputs produced. Because of its practical importance and theoretical interest, the problem of testing finite state machines has been studied in different areas and at various times. The earliest published literature on this topic dates back to the 50’s. Activities in the 60’s and early 70’s were motivated mainly by automata theory and sequential circuit testing. The area seemed to have mostly died down until a few years ago when the testing problem was resurrected and is now being studied anew due to its applications to conformance testing of communication protocols. While some old problems which had been open for decades were resolved recently, new concepts and more intriguing problems from new applications emerge. We review the fundamental problems in testing finite state machines and techniques for solving these problems, tracing progress in the area from its inception to the present and the state of the art. In addition, we discuss extensions of finite state machines and some other topics related to testing.
A complexity theoretic approach to randomness, in
 Proceedings of the 15th Annual ACM Symposium on Theory of Computing
, 1983
"... Abstract: We study a time bounded variant of Kolmogorov complexity. This motion, together with universal hashing, can be used to show that problems solvable probabilistically in polynomial time are all within the second level of the polynomial time hierarchy. We also discuss applications to the the ..."
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Cited by 157 (1 self)
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Abstract: We study a time bounded variant of Kolmogorov complexity. This motion, together with universal hashing, can be used to show that problems solvable probabilistically in polynomial time are all within the second level of the polynomial time hierarchy. We also discuss applications to the theory of probabilistic constructions. I.
OneDimensional Quantum Walks
 STOC'01
, 2001
"... We define and analyze quantum computational variants of random walks on onedimensional lattices. In particular, we analyze a quantum analog of the symmetric random walk, which we call the Hadamard walk. Several striking differences between the quantum and classical cases are observed. For example, ..."
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Cited by 140 (10 self)
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We define and analyze quantum computational variants of random walks on onedimensional lattices. In particular, we analyze a quantum analog of the symmetric random walk, which we call the Hadamard walk. Several striking differences between the quantum and classical cases are observed. For example, when unrestricted in either direction, the Hadamard walk has position that is nearly uniformly distributed in the range [\Gamma t= p
A random walk construction of uniform spanning trees and uniform labelled trees
 SIAM Journal on Discrete Mathematics
, 1990
"... Abstract A random walk on a finite graph can be used to construct a uniformrandom spanning tree. We show how random walk techniques can be applied to the study of several properties of the uniform randomspanning tree: the proportion of leaves, the distribution of degrees, and the diameter. ..."
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Cited by 102 (4 self)
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Abstract A random walk on a finite graph can be used to construct a uniformrandom spanning tree. We show how random walk techniques can be applied to the study of several properties of the uniform randomspanning tree: the proportion of leaves, the distribution of degrees, and the diameter.
Diversitybased Inference of Finite Automata
 Journal of ACM
, 1994
"... Abstract. We present new procedures for inferring the structure of a finitestate automaton (FSA) from its input \ output behavior, using access to the automaton to perform experiments. Our procedures use a new representation for finite automata, based on the notion of equivalence between tesfs. We ..."
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Cited by 85 (2 self)
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Abstract. We present new procedures for inferring the structure of a finitestate automaton (FSA) from its input \ output behavior, using access to the automaton to perform experiments. Our procedures use a new representation for finite automata, based on the notion of equivalence between tesfs. We call the number of such equivalence classes the diLersL@of the automaton; the diversity may be as small as the logarithm of the number of states of the automaton. For the special class of pennatatton aatornata, we describe an inference procedure that runs in time polynomial in the diversity and log(l/6), where 8 is a given upper bound on the probability that our procedure returns an incorrect result. (Since our procedure uses randomization to perform experiments, there is a certain controllable chance that it will return an erroneous result.) We also discuss techniques for handling more general automata. We present evidence for the practical efficiency of our approach. For example, our procedure is able to infer the structure of an automaton based on Rubik’s Cube (which has approximately 10 lY states) in about 2 minutes on a DEC MicroVax. This automaton is many orders of magnitude larger than possible with previous techniques, which would require time proportional at least to the number of global states. (Note that in this example, only a small fraction (1014, of the global
Distributed covering by antrobots using evaporating traces
 IEEE Transactions on Robotics and Automation
, 1999
"... Abstract—Ants and other insects are known to use chemicals called pheromones for various communication and coordination tasks. In this paper, we investigate the ability of a group of robots, that communicate by leaving traces, to perform the task of cleaning the floor of an unmapped building, or an ..."
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Cited by 81 (1 self)
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Abstract—Ants and other insects are known to use chemicals called pheromones for various communication and coordination tasks. In this paper, we investigate the ability of a group of robots, that communicate by leaving traces, to perform the task of cleaning the floor of an unmapped building, or any task that requires the traversal of an unknown region. More specifically, we consider robots which leave chemical odor traces that evaporate with time, and are able to evaluate the strength of smell at every model is a decentralized multiagent adaptive system with a shared memory, moving on a graph whose vertices are the floortiles. We describe three methods of covering a graph in a distributed fashion, using smell traces that gradually vanish with time, and show that they all result in eventual task completion, two of them in a time polynomial in the number of tiles. As opposed to existing traversal methods (e.g., depth first search), our algorithms are adaptive: they will complete the traversal of the graph even if some of the a(ge)nts die or the graph changes (edges/vertices added or deleted) during the execution, as long as the graph stays connected. Another advantage of our agent interaction processes is the ability of agents to use noisy information at the cost of longer cover time. Index Terms—Antrobotics, covering, exploration, multiagent systems, robotics.
Two applications of inductive counting for complementation problems
 SIAM JOURNAL OF COMPUTING
, 1989
"... ... nondeterministic spacebounded complexity classes are closed under complementation, two further applications of the inductive counting technique are developed. First, an errorless probabilistic algorithm for the undirected graph st connectivity problem that runs in O(log n) space and polynomial ..."
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Cited by 62 (3 self)
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... nondeterministic spacebounded complexity classes are closed under complementation, two further applications of the inductive counting technique are developed. First, an errorless probabilistic algorithm for the undirected graph st connectivity problem that runs in O(log n) space and polynomial expected time is given. Then it is shown that the class LOGCFL is closed under complementation. The latter is a special case of a general result that shows closure under complementation of classes defined by semiunbounded fanin circuits (or, equivalently, nondeterministic auxiliary pushdown automata or treesize bounded alternating Turing machines). As one consequence, it is shown that small numbers of "role switches" in twoperson pebbling can be eliminated.
A Tight Upper Bound on the Cover Time for Random Walks on Graphs
, 1995
"... We prove that the expected time for a random walk to visit all n vertices of a connected graph is at most 4 27 n 3 + o(n 3 ). 1 Introduction Let G = G(V; E) be a simple connected undirected graph with n vertices and m edges. We consider simple random walks on G, where at each step the rand ..."
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Cited by 59 (7 self)
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We prove that the expected time for a random walk to visit all n vertices of a connected graph is at most 4 27 n 3 + o(n 3 ). 1 Introduction Let G = G(V; E) be a simple connected undirected graph with n vertices and m edges. We consider simple random walks on G, where at each step the random walk moves to a vertex chosen at random with uniform probability from the neighbors of the current vertex. Let u and v denote two vertices. The hitting time H[u; v] is the expected number of steps it takes a walk that starts at u to reach v. The commute time C[u; v] is the expected number of steps that it takes a walk to go from u to v and back to u (that is, C[u; v] = H[u; v] +H[v;u]). The cover time EC[v] is the expected number of steps it takes a random walk that starts at v to visit all vertices of the graph. For a graph G(V; E) its hitting time H[G] (commute time C[G], cover time EC[G], respectively) is defined as H[G] = max u;v2V [H[u; v]] (C[G] = max u;v2V [C[u; v]] , EC[G] = max v...