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Local Parallel Model Checking for the Alternation Free µCalculus
 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS’01), volume 2031 of LNCS
, 2001
"... In this paper, we describe the design and implementation of (several ... ..."
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Cited by 32 (6 self)
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In this paper, we describe the design and implementation of (several ...
Graph Ramsey theory and the polynomial hierarchy (extended abstract
 Annual ACM Symposium on Theory of Computing (Atlanta, GA, 1999), ACM
, 1999
"... In the Ramsey theory ofgraphs F + (G, H) means that for every way of coloring the edges of F red and blue F will contain either a red G or a blue H. The problem ARROWING of deciding whether F + (G, H) lies in II; = coNPNP and it was shown to be coNP hard by Burr [5]. We prove that ARROWING is actua ..."
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Cited by 19 (4 self)
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In the Ramsey theory ofgraphs F + (G, H) means that for every way of coloring the edges of F red and blue F will contain either a red G or a blue H. The problem ARROWING of deciding whether F + (G, H) lies in II; = coNPNP and it was shown to be coNP hard by Burr [5]. We prove that ARROWING is actually II;complete, simultaneously settling a conjecture of Burr and providing a natural example of a problem complete for a higher level of the polynomial hierarchy. We also show that STRONG ARROWING, the version for induced subgraphs, is rI;complete. 1
Optimal strategies for testing nondeterministic systems
 In ISSTA’04, volume 29 of Software Engineering Notes
, 2004
"... This paper deals with testing of nondeterministic software systems. We assume that a model of the nondeterministic system is given by a directed graph with two kind of vertices: states and choice points. Choice points represent the nondeterministic behaviour of the implementation under test (IUT). E ..."
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Cited by 19 (6 self)
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This paper deals with testing of nondeterministic software systems. We assume that a model of the nondeterministic system is given by a directed graph with two kind of vertices: states and choice points. Choice points represent the nondeterministic behaviour of the implementation under test (IUT). Edges represent transitions. They have costs and probabilities. Test case generation in this setting amounts to generation of a game strategy. The two players are the testing tool (TT) and the IUT. The game explores the graph. The TT leads the IUT by selecting an edge at the state vertices. At the choice points the control goes to the IUT. A game strategy decides which edge should be taken by the TT in each state. This paper presents three novel algorithms 1) to determine an optimal strategy for the bounded reachability game, where optimality means maximizing the probability to reach any of the given final states from a given start state while at the same time minimizing the costs of traversal; 2) to determine a winning strategy for the bounded reachability game, which guarantees that given final vertices are reached, regardless how the IUT reacts; 3) to determine a fast converging edge covering strategy, which guarantees that the probability to cover all edges quickly converges to 1 if TT follows the strategy.
On Distributing Symmetric Streaming Computations
"... A common approach for dealing with large data sets is to stream over the input in one pass, and perform computations using sublinear resources. For truly massive data sets, however, even making a single pass over the data is prohibitive. Therefore, streaming computations must be distributed over man ..."
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Cited by 19 (1 self)
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A common approach for dealing with large data sets is to stream over the input in one pass, and perform computations using sublinear resources. For truly massive data sets, however, even making a single pass over the data is prohibitive. Therefore, streaming computations must be distributed over many machines. In practice, obtaining significant speedups using distributed computation has numerous challenges including synchronization, load balancing, overcoming processor failures, and data distribution. Successful systems in practice such as Google’s MapReduce and Apache’s Hadoop address these problems by only allowing a certain class of highly distributable tasks defined by local computations that can be applied in any order to the input. The fundamental question that arises is: How does the class of computational tasks supported by these systems differ from the class for which streaming solutions exist? We introduce a simple algorithmic model for massive, unordered, distributed (mud) computation, as implemented by these systems. We show that in principle, mud algorithms are equivalent in power to symmetric streaming algorithms. More precisely, we show that any symmetric (orderinvariant) function that can be computed by a streaming algorithm can also be computed by a mud algorithm, with comparable space and communication complexity. Our simulation uses Savitch’s theorem and therefore has superpolynomial time complexity. We extend our simulation result to some natural classes of approximate and randomized streaming algorithms. We also give negative results, using communication complexity arguments to prove that extensions to private randomness, promise problems and indeterminate functions are impossible. We also introduce an extension of the mud model to multiple keys and multiple rounds. 1
Querying and Embedding Compressed Texts
, 2005
"... Abstract. In this work the computational complexity of two simple string problems on compressed input strings is considered: the querying problem (What is the symbol at a given position in a given input string?) and the embedding problem (Can the first input string embedded into the second input str ..."
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Cited by 11 (4 self)
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Abstract. In this work the computational complexity of two simple string problems on compressed input strings is considered: the querying problem (What is the symbol at a given position in a given input string?) and the embedding problem (Can the first input string embedded into the second input string?). Straightline programs are used for text compression. It is shown that the querying problem becomes Pcomplete for compressed strings, while the embedding problem becomes hard for the complexity class Θ p 2. 1
On Computational Complexity of Basic Decision Problems of Finite Tree Automata
, 1997
"... This report focuses on the following basic decision problems of finite tree automata: nonemptiness and intersection nonemptiness. There is a comprehensive proof of EXPTIMEcompleteness of the intersection nonemptiness problem, and it is shown that the nonemptiness problem is Pcomplete. A notion of ..."
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Cited by 10 (3 self)
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This report focuses on the following basic decision problems of finite tree automata: nonemptiness and intersection nonemptiness. There is a comprehensive proof of EXPTIMEcompleteness of the intersection nonemptiness problem, and it is shown that the nonemptiness problem is Pcomplete. A notion of succinctness is considered with respect to which the intersection nonemptiness problem is in fact a succinct version of the nonemptiness problem. The report includes a short survey of closely related problems which shows that there is a rule of thumb: if a decision problem for (deterministic) finite automata is complete for a certain space complexity then the same decision problem for (deterministic) finite tree automata is complete for the corresponding alternating space complexity, but alternating space is precisely deterministic time, only one exponential higher. 1 Introduction Finite tree automata [14, 51] is a natural generalization of classical finite automata to automata that acce...
The Decidability of Simultaneous Rigid EUnification with One Variable
 REWRITING TECHNIQUES AND APPLICATIONS
, 1997
"... We show that simultaneous rigid Eunification, or SREU for short, is decidable and in fact EXPTIMEcomplete in the case of one variable. This result implies that the ... fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the ..."
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Cited by 10 (10 self)
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We show that simultaneous rigid Eunification, or SREU for short, is decidable and in fact EXPTIMEcomplete in the case of one variable. This result implies that the ... fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the 99fragment, we obtain a complete classification of decidability of the prenex fragment of intuitionistic logic with equality, in terms of the quantifier prefix. It is also proved that SREU with one variable and a constant bound on the number of rigid equations is Pcomplete.
Small weakly universal Turing machines
"... Abstract. We give small universal Turing machines with statesymbol pairs of (6, 2), (3,3) and (2,4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest ..."
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Cited by 7 (4 self)
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Abstract. We give small universal Turing machines with statesymbol pairs of (6, 2), (3,3) and (2,4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest known weakly universal Turing machines. Despite their small size these machines are efficient polynomial time simulators of Turing machines. 1
Symbolic model checking for temporalepistemic logics
 ACM SIGACT News
, 2007
"... Abstract. We survey some of the recent work in verification via symbolic model checking of temporalepistemic logic. Specifically, we discuss OBDDbased and SATbased approaches for epistemic logic built on discrete and realtime branching time temporal logic. The underlying semantical model conside ..."
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Cited by 6 (1 self)
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Abstract. We survey some of the recent work in verification via symbolic model checking of temporalepistemic logic. Specifically, we discuss OBDDbased and SATbased approaches for epistemic logic built on discrete and realtime branching time temporal logic. The underlying semantical model considered throughout is the one of interpreted system, suitably extended whenever necessary. 1