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224
Randomized Algorithms
, 1995
"... Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simp ..."
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Cited by 2183 (38 self)
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Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simplest, or both. A randomized algorithm is an algorithm that uses random numbers to influence the choices it makes in the course of its computation. Thus its behavior (typically quantified as running time or quality of output) varies from
On the Synthesis of Discrete Controllers for Timed Systems
 in E.W. Mayr and C. Puech (Eds), Proc. STACS'95, LNCS 900
, 1995
"... Abstract. This paper presents algorithms for the automatic synthesis of realtime controllers by nding a winning strategy for certain games de ned by the timedautomata of Alur and Dill. In such games, the outcome depends on the players ' actions as well as on their timing. We believe that thes ..."
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Cited by 236 (18 self)
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Abstract. This paper presents algorithms for the automatic synthesis of realtime controllers by nding a winning strategy for certain games de ned by the timedautomata of Alur and Dill. In such games, the outcome depends on the players ' actions as well as on their timing. We believe that these results will pave theway for the application of program synthesis techniques to the construction of realtime embedded systems from their speci cations. 1
Optimal lower bounds for quantum automata and random access codes
"... Consider the finite regular ¢¤£¦¥¨§�©�����©�� language ©������� �. In [3] it was shown that while this language is accepted by a deterministic finite automaton of ������ � size, any oneway quantum finite automaton (QFA) for it has ���¤ � £��� � ����£� � size. This was based on the fact that the e ..."
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Cited by 121 (9 self)
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Consider the finite regular ¢¤£¦¥¨§�©�����©�� language ©������� �. In [3] it was shown that while this language is accepted by a deterministic finite automaton of ������ � size, any oneway quantum finite automaton (QFA) for it has ���¤ � £��� � ����£� � size. This was based on the fact that the evolution of a QFA is required to be reversible. When arbitrary intermediate measurements are allowed, this intuition breaks down. Nonetheless, we show ���� � £�� a lower bound for such QFA ¢ £ for, thus also improving the previous bound. The improved bound is obtained from simple entropy arguments based on Holevo’s theorem [8]. This method also allows us to obtain an asymptotically op���������������� � timal bound for the dense quantum codes (random access codes) introduced in [3]. We then turn to Holevo’s theorem, and show that in typical situations, it may be replaced by a tighter and more transparent inprobability bound.
Algebraic Reasoning for Probabilistic Concurrent Systems
 Proc. IFIP TC2 Working Conference on Programming Concepts and Methods
, 1990
"... We extend Milner's SCCS to obtain a calculus, PCCS, for reasoning about communicating probabilistic processes. In particular, the nondeterministic process summation operator of SCCS is replaced with a probabilistic one, in which the probability of behaving like a particular summand is given exp ..."
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Cited by 116 (5 self)
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We extend Milner's SCCS to obtain a calculus, PCCS, for reasoning about communicating probabilistic processes. In particular, the nondeterministic process summation operator of SCCS is replaced with a probabilistic one, in which the probability of behaving like a particular summand is given explicitly. The operational semantics for PCCS is based on the notion of probabilistic derivation, and is given structurally as a set of inference rules. We then present an equational theory for PCCS based on probabilistic bisimulation, an extension of Milner's bisimulation proposed by Larsen and Skou. We provide the first axiomatization of probabilistic bisimulation, a subset of which is relatively complete for finitestate probabilistic processes. In the probabilistic case, a notion of processes with almost identical behavior (i.e., with probability 1 \Gamma ffl, for ffl sufficiently small) appears to be more useful in practice than a notion of equivalence, since the latter is often too restricti...
On the Power of Quantum Finite State Automata
 Proceedings of the 38th IEEE Conference on Foundations of Computer Science
, 1997
"... In this paper, we introduce 1way and 2way quantum finite state automata (1qfa's and 2qfa's), which are the quantum analogues of deterministic, nondeterministic and probabilistic 1way and 2way finite state automata. We prove the following facts regarding 2qfa's. 1. For any ffl ? 0, ..."
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Cited by 106 (6 self)
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In this paper, we introduce 1way and 2way quantum finite state automata (1qfa's and 2qfa's), which are the quantum analogues of deterministic, nondeterministic and probabilistic 1way and 2way finite state automata. We prove the following facts regarding 2qfa's. 1. For any ffl ? 0, there is a 2qfa M which recognizes the nonregular language L = fa m b m j m 1g with (onesided) error bounded by ffl, and which halts in linear time. Specifically, M accepts any string in L with probability 1 and rejects any string not in L with probability at least 1 \Gamma ffl. 2. For every regular language L, there is a reversible (and hence quantum) 2way finite state automaton which recognizes L and which runs in linear time. In fact, it is possible to define 2qfa's which recognize the noncontextfree language fa m b m c m jm 1g, based on the same technique used for 1. Consequently, the class of languages recognized by linear time, bounded error 2qfa's properly includes the regular l...
The Computational Complexity of Probabilistic Planning
 Journal of Artificial Intelligence Research
, 1998
"... We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and loopin ..."
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Cited by 90 (6 self)
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We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and looping plans, and partially ordered plans under three natural definitions of plan value. We show that problems of interest are complete for a variety of complexity classes: PL, P, NP, coNP, PP, NP PP, coNP PP , and PSPACE. In the process of proving that certain planning problems are complete for NP PP , we introduce a new basic NP PP complete problem, EMajsat, which generalizes the standard Boolean satisfiability problem to computations involving probabilistic quantities; our results suggest that the development of good heuristics for EMajsat could be important for the creation of efficient algorithms for a wide variety of problems.
On the Undecidability of Probabilistic Planning and Related Stochastic Optimization Problems
 Artificial Intelligence
, 2003
"... Automated planning, the problem of how an agent achieves a goal given a repertoire of actions, is one of the foundational and most widely studied problems in the AI literature. The original formulation of the problem makes strong assumptions regarding the agent's knowledge and control over the ..."
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Cited by 69 (0 self)
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Automated planning, the problem of how an agent achieves a goal given a repertoire of actions, is one of the foundational and most widely studied problems in the AI literature. The original formulation of the problem makes strong assumptions regarding the agent's knowledge and control over the world, namely that its information is complete and correct, and that the results of its actions are deterministic and known.
Characterizations of 1Way Quantum Finite Automata
 SIAM Journal on Computing
"... The 2way quantum finite automaton introduced by Kondacs and Watrous[KW97] can accept nonregular languages with bounded error in polynomial time. If we restrict the head of the automaton to moving classically and to moving only in one direction, the acceptance power of this 1way quantum finite aut ..."
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Cited by 55 (0 self)
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The 2way quantum finite automaton introduced by Kondacs and Watrous[KW97] can accept nonregular languages with bounded error in polynomial time. If we restrict the head of the automaton to moving classically and to moving only in one direction, the acceptance power of this 1way quantum finite automaton is reduced to a proper subset of the regular languages. In this paper we study two different models of 1way quantum finite automata. The first model, termed measureonce quantum finite automata, was introduced by Moore and Crutchfield[MCar], and the second model, termed measuremany quantum finite automata, was introduced by Kondacs and Watrous[KW97]. We characterize the measureonce model when it is restricted to accepting with bounded error and show that, without that restriction, it can solve the word problem over the free group. We also show that it can be simulated by a probabilistic finite automaton and describe an algorithm that determines if two measureonce automata are equiv...
Computing Minimum and Maximum Reachability Times in Probabilistic Systems
, 1999
"... A Markov decision process is a generalization of a Markov chain in which both probabilistic and nondeterministic choice coexist. Given a Markov decision process with costs associated with the transitions and a set of target states, the stochastic shortest path problem consists in computing the minim ..."
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Cited by 54 (2 self)
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A Markov decision process is a generalization of a Markov chain in which both probabilistic and nondeterministic choice coexist. Given a Markov decision process with costs associated with the transitions and a set of target states, the stochastic shortest path problem consists in computing the minimum expected cost of a control strategy that guarantees to reach the target. In this paper, we consider the classes of stochastic shortest path problems in which the costs are all nonnegative, or all nonpositive. Previously, these two classes of problems could be solved only under the assumption that the policies that minimize or maximize the expected cost also lead to the target with probability 1. This assumption does not necessarily hold for Markov decision processes that arise as model for distributed probabilistic systems. We present efficient methods for solving these two classes of problems without relying on additional assumptions. The methods are based on algorithms to transform th...
Quantum automata and quantum grammars
 Theoretical Computer Science
"... Abstract. To study quantum computation, it might be helpful to generalize structures from language and automata theory to the quantum case. To that end, we propose quantum versions of finitestate and pushdown automata, and regular and contextfree grammars. We find analogs of several classical the ..."
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Cited by 51 (2 self)
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Abstract. To study quantum computation, it might be helpful to generalize structures from language and automata theory to the quantum case. To that end, we propose quantum versions of finitestate and pushdown automata, and regular and contextfree grammars. We find analogs of several classical theorems, including pumping lemmas, closure properties, rational and algebraic generating functions, and Greibach normal form. We also show that there are quantum contextfree languages that are not contextfree. 1