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27
Pointsto analysis using BDDs
 In Programming Language Design and Implementation (PLDI
, 2003
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An algorithm for strongly connected component analysis in n log n symbolic steps
 Formal Methods in System Design
"... Abstract. We present a symbolic algorithm for strongly connected component decomposition. The algorithm performs �(n log n) image and preimage computations in the worst case, where n is the number of nodes in the graph. This is an improvement over the previously known quadratic bound. The algorithm ..."
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Cited by 61 (6 self)
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Abstract. We present a symbolic algorithm for strongly connected component decomposition. The algorithm performs �(n log n) image and preimage computations in the worst case, where n is the number of nodes in the graph. This is an improvement over the previously known quadratic bound. The algorithm can be used to decide emptiness of Büchi automata with the same complexity bound, improving Emerson and Lei’s quadratic bound, and emptiness of Streett automata, with a similar bound in terms of nodes. It also leads to an improved procedure for the generation of nonemptiness witnesses.
A Comparative Study of Symbolic Algorithms for the Computation of Fair Cycles
"... Detection of fair cycles is an important task of many model checking algorithms. When the transition system is represented symbolically, the standard approach to fair cycle detection is the one of Emerson and Lei. In the last decade variants of this algorithm and an alternative method based on stron ..."
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Cited by 41 (7 self)
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Detection of fair cycles is an important task of many model checking algorithms. When the transition system is represented symbolically, the standard approach to fair cycle detection is the one of Emerson and Lei. In the last decade variants of this algorithm and an alternative method based on strongly connected component decomposition have been proposed. We present a taxonomy of these techniques and compare representatives of each major class on a collection of reallife examples. Our results indicate that the EmersonLei procedure is the fastest, but other algorithms tend to generate shorter counterexamples.
Structural symbolic CTL model checking of asynchronous systems
 Computer Aided Verification (CAV’03), LNCS 2725
, 2003
"... Abstract. In previous work, we showed how structural information can be used to efficiently generate the statespace of asynchronous systems. Here, we apply these ideas to symbolic CTL model checking. Thanks to a Kronecker encoding of the transition relation, we detect and exploit event locality and ..."
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Cited by 20 (11 self)
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Abstract. In previous work, we showed how structural information can be used to efficiently generate the statespace of asynchronous systems. Here, we apply these ideas to symbolic CTL model checking. Thanks to a Kronecker encoding of the transition relation, we detect and exploit event locality and apply better fixedpoint iteration strategies, resulting in ordersofmagnitude reductions for both execution times and memory consumption in comparison to wellestablished tools such as NuSMV. 1
Design and evaluation of a symbolic and abstractionbased model checker
 Taiwan University
, 2004
"... Abstract. Symbolic modelchecking usually includes two steps: the building of a compact representation of a state graph and the evaluation of the properties of the system upon this data structure. In case of properties expressed with a linear time logic, it appears that the second step is often more ..."
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Cited by 13 (7 self)
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Abstract. Symbolic modelchecking usually includes two steps: the building of a compact representation of a state graph and the evaluation of the properties of the system upon this data structure. In case of properties expressed with a linear time logic, it appears that the second step is often more time consuming than the first one. In this work, we present a mixed solution which builds an observation graph represented in a non symbolic way but where the nodes are essentially symbolic set of states. Due to the small number of events to be observed in a typical formula, this graph has a very moderate size and thus the complexity time of verification is neglectible w.r.t. the time to build the observation graph. Thus we propose different symbolic implementations for the construction of the nodes of this graph. The evaluations we have done on standard examples show that our method outperforms the pure symbolic methods which makes it attractive.
A Symbolic Approach to the AllPairs ShortestPaths Problem
 In WG 2004, LNCS 3353
, 2004
"... Abstract. Graphs can be represented symbolically by the Ordered Binary Decision Diagram (OBDD) of their characteristic function. To solve problems in such implicitly given graphs, specialized symbolic algorithms are needed which are restricted to the use of functional operations offered by the OBDD ..."
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Cited by 9 (5 self)
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Abstract. Graphs can be represented symbolically by the Ordered Binary Decision Diagram (OBDD) of their characteristic function. To solve problems in such implicitly given graphs, specialized symbolic algorithms are needed which are restricted to the use of functional operations offered by the OBDD data structure. In this paper, a symbolic algorithm for the allpairs shortestpaths (APSP) problem in loopless directed graphs with strictly positive integral edge weights is presented. It requires Θ ( log 2 (NB) ) OBDDoperations to obtain the lengths and edges of all shortest paths in graphs with N nodes and maximum edge weight B. It is proved that runtime and space usage are polylogarithmic w. r. t. N and B on graph sequences with characteristic boundedwidth functions. This convenient property is closed under certain graph composition operations. Moreover, an alternative symbolic approach for general integral edge weights is sketched which does not behave efficiently on general graph sequences with boundedwidth functions. Finally, two variants of theAPSPproblemarebrieflydiscussed. 1
Deriving Symbolic Representations from Stochastic Process Algebras
, 2002
"... A new denotational semantics for a variant of the stochastic process algebra TIPP is presented, which maps process terms to Multiterminal binary decision diagrams. It is shown that the new semantics is Markovian bisimulation equivalent to the standard SOS semantics. The paper also addresses the ..."
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Cited by 9 (5 self)
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A new denotational semantics for a variant of the stochastic process algebra TIPP is presented, which maps process terms to Multiterminal binary decision diagrams. It is shown that the new semantics is Markovian bisimulation equivalent to the standard SOS semantics. The paper also addresses the difficult question of keeping the underlying state space minimal at every construction step.
Biconnectivity on symbolically represented graphs: A linear solution
 IN ISAAC 2003, VOLUME 2906 OF LNCS
, 2003
"... We define an algorithm for determining, in a linear number of symbolic steps, the biconnected components of a graph implicitly represented with Ordered Binary Decision Diagrams (OBDDs). Working on symbolically represented data has potential: the standards achieved in graph sizes (playing a crucial ..."
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Cited by 9 (1 self)
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We define an algorithm for determining, in a linear number of symbolic steps, the biconnected components of a graph implicitly represented with Ordered Binary Decision Diagrams (OBDDs). Working on symbolically represented data has potential: the standards achieved in graph sizes (playing a crucial role, for example, in verification, VLSI design, and CAD) are definitely higher. On the other hand, symbolic algorithm’s design generates constraints as well. For example, Depth First Search is not feasible in the symbolic setting, and our algorithm relies on the use of spinesets, introduced in [8] for strongly connected components, as its substitute. Our approach suggests a symbolic framework to tackle those problems which are naturally solved by a DFSbased algorithm in the standard case.
Exponential Lower Bounds on the Space Complexity of OBDDBased Graph Algorithms
, 2006
"... Ordered Binary Decision Diagrams (OBDDs) are a data structure for Boolean functions which is successfully applied in many areas like Integer Programming, Model Checking, and Relational Algebra. Nevertheless, many basic graph problems like Connectivity, Reachability, SingleSource ShortestPaths, a ..."
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Cited by 3 (0 self)
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Ordered Binary Decision Diagrams (OBDDs) are a data structure for Boolean functions which is successfully applied in many areas like Integer Programming, Model Checking, and Relational Algebra. Nevertheless, many basic graph problems like Connectivity, Reachability, SingleSource ShortestPaths, and Flow Maximization are known to be PSPACEhard if their input graphs are represented by OBDDs. This holds even for input OBDDs of constant width. We extend these results by concrete exponential lower bounds on the space complexity of OBDDbased algorithms for the Reachability Problem, the SingleSource ShortestPaths Problem, and the Maximum Flow Problem. This involves the first exponential lower bound on the OBDD size for the highest bit of Integer Multiplication w. r. t. the natural interleaved variable order.