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Efficient Simplification of Bisimulation Formulas
 In Proceedings of the Workshop on Tools and Algorithms for the Construction and Analysis of Systems, pages 111132. LNCS 1019
, 1995
"... The problem of checking or optimally simplifying bisimulation formulas is likely to be computationally very hard. We take a different view at the problem: we set out to define a very fast algorithm, and then see what we can obtain. Sometimes our algorithm can simplify a formula perfectly, sometimes ..."
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The problem of checking or optimally simplifying bisimulation formulas is likely to be computationally very hard. We take a different view at the problem: we set out to define a very fast algorithm, and then see what we can obtain. Sometimes our algorithm can simplify a formula perfectly, sometimes it cannot. However, the algorithm is extremely fast and can, therefore, be added to formulabased bisimulation model checkers at practically no cost. When the formula can be simplified by our algorithm, this can have a dramatic positive effect on the better, but also more time consuming, theorem provers which will finish the job. 1 Introduction The need for validity checking or optimal simplification of first order bisimulation formulas has arisen from recent work on symbolic bisimulation checking of valuepassing calculi [4, 9, 15]. The NPcompleteness of checking satisfiability of propositional formulas [3] implies that validity checking of that class of formulas is coNP complete. Addit...
A New Algorithm for Building Alphabetic Minimax Trees
, 2008
"... We show how to build an alphabetic minimax tree for a sequence W = w1,...,wn of real weights in O(nd log log n) time, where d is the number of distinct integers ⌈wi⌉. We apply this algorithm to building an alphabetic prefix code given a sample. ..."
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We show how to build an alphabetic minimax tree for a sequence W = w1,...,wn of real weights in O(nd log log n) time, where d is the number of distinct integers ⌈wi⌉. We apply this algorithm to building an alphabetic prefix code given a sample.
Dynamic 2Connectivity With Backtracking
, 1998
"... . We give algorithms and data structures that maintain the 2edge and 2vertexconnected components of a graph under insertions and deletions of edges and vertices, where deletions occur in a backtracking fashion (i.e., deletions undo the insertions in the reverse order). Our algorithms ru ..."
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.<F3.83e+05> We give algorithms and data structures that maintain the 2edge and 2vertexconnected components of a graph under insertions and deletions of edges and vertices, where deletions occur in a backtracking fashion (i.e., deletions undo the insertions in the reverse order). Our algorithms run in #(log<F3.054e+05><F3.83e+05> n) worstcase time per operation and use<F3.054e+05><F3.83e+05> #(n) space, where<F3.054e+05> n<F3.83e+05> is the number of vertices. Using our data structure we can answer queries, which ask whether vertices<F3.054e+05> u<F3.83e+05> and<F3.054e+05> v<F3.83e+05> belong to the same 2connected component, in #(log<F3.054e+05><F3.83e+05> n) worstcase time.<F4.005e+05> Key words.<F3.83e+05> dynamic graph algorithms, backtracking<F4.005e+05> AMS subject classifications.<F3.83e+05> 68Q20, 68Q25<F4.005e+05> PII.<F3.83e+05> S0097539794272582<F5.251e+05> 1. Introduction.<F4.483e+05> Dynamic graph problems have been studied extensively in the last several years. Rou...
Backtracking
"... Contents 1 Introduction 3 2 Models of computation 6 3 The Set Union Problem 9 4 The WorstCase Time Complexity of a Single Operation 15 5 The Set Union Problem with Deunions 18 6 Split and the Set Union Problem on Intervals 22 7 The Set Union Problem with Unlimited Backtracking 26 1 Introduction A ..."
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Contents 1 Introduction 3 2 Models of computation 6 3 The Set Union Problem 9 4 The WorstCase Time Complexity of a Single Operation 15 5 The Set Union Problem with Deunions 18 6 Split and the Set Union Problem on Intervals 22 7 The Set Union Problem with Unlimited Backtracking 26 1 Introduction An equivalence relation on a finite set S is a binary relation that is reflexive symmetric and transitive. That is, for s; t and u in S, we have that sRs, if sRt then tRs, and if sRt and tRu then sRu. Set S is partitioned by R into equivalence classes where each class cointains all and only the elements that obey R pairwise. Many computational problems involve representing, modifying and tracking the evolution of equivalenc
Retroactive data structures (extended abstract)
 IN SODA ’04: PROCEEDINGS OF THE FIFTEENTH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 2004
"... We introduce a new data structuring paradigm in which operations can be performed on a data structure not only in the present but also in the past. In this new paradigm, called retroactive data structures, the historical sequence of operations performed on the data structure is not fixed. The data s ..."
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We introduce a new data structuring paradigm in which operations can be performed on a data structure not only in the present but also in the past. In this new paradigm, called retroactive data structures, the historical sequence of operations performed on the data structure is not fixed. The data structure allows arbitrary insertion and deletion of operations at arbitrary times, subject only to consistency requirements. We initiate the study of retroactive data structures by formally defining the model and its variants. We prove that, unlike persistence, efficient retroactivity is not always achievable, so we go on to present several specific retroactive data structures.