Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Introduction to algorithms
Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
High performance BDD package by exploiting memory hierarchy
DAC '96 Proceedings of the 33rd annual Design Automation Conference
Symbolic manipulation of Boolean functions using a graphical representation
DAC '85 Proceedings of the 22nd ACM/IEEE Design Automation Conference
Implicit enumeration of strongly connected components
ICCAD '99 Proceedings of the 1999 IEEE/ACM international conference on Computer-aided design
A New Heuristic for Bad Cycle Detection Using BDDs
Formal Methods in System Design - Special issue on CAV '97
Symbolic Model Checking
Algorithms and Data Structures in VLSI Design
Algorithms and Data Structures in VLSI Design
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A Comparative Study of Symbolic Algorithms for the Computation of Fair Cycles
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
Is There a Best Symbolic Cycle-Detection Algorithm?
TACAS 2001 Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
Markovian analysis of large finite state machines
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
An efficient algorithm for computing bisimulation equivalence
Theoretical Computer Science
Ackermann encoding, bisimulations and OBDDs
Theory and Practice of Logic Programming
An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps
Formal Methods in System Design
Compositional SCC Analysis for Language Emptiness
Formal Methods in System Design
From complementation to certification
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
Lower bounds on the OBDD size of two fundamental functions' graphs
Information Processing Letters
Finding strongly connected components in parallel using O(log2n) reachability queries
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
A note on the size of OBDDs for the graph of integer multiplication
Information Processing Letters
On the OBDD Complexity of Threshold Functions and the Variable Ordering Problem
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
On the size of (generalized) OBDDs for threshold functions
Information Processing Letters
Larger Lower Bounds on the OBDD Complexity of Integer Multiplication
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Symbolic OBDD-Based Reachability Analysis Needs Exponential Space
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Automata-theoretic model checking revisited
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Dynamical properties of timed automata revisited
FORMATS'07 Proceedings of the 5th international conference on Formal modeling and analysis of timed systems
A hybrid algorithm for LTL games
VMCAI'08 Proceedings of the 9th international conference on Verification, model checking, and abstract interpretation
Exponential space complexity for OBDD-based reachability analysis
Information Processing Letters
Exponential space complexity for symbolic maximum flow algorithms in 0-1 networks
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
On symbolic OBDD-based algorithms for the minimum spanning tree problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Larger lower bounds on the OBDD complexity of integer multiplication
Information and Computation
The quest for a tight translation of büchi to co-büchi automata
Fields of logic and computation
Symbolic algorithms for qualitative analysis of Markov decision processes with Buchi objectives
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
The complexity of problems on implicitly represented inputs
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
A larger lower bound on the OBDD complexity of the most significant bit of multiplication
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Lower bounds on the OBDD size of graphs of some popular functions
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
On symbolic scheduling independent tasks with restricted execution times
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
A symbolic approach to the all-pairs shortest-paths problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Exponential lower bounds on the space complexity of OBDD-Based graph algorithms
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
An efficient implicit OBDD-Based algorithm for maximal matchings
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
On symbolic OBDD-based algorithms for the minimum spanning tree problem
Theoretical Computer Science
Implicit computation of maximum bipartite matchings by sublinear functional operations
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
A Lightweight Method for Automated Design of Convergence in Network Protocols
ACM Transactions on Autonomous and Adaptive Systems (TAAS) - Special Section: Extended Version of SASO 2011 Best Paper
Symbolic algorithms for qualitative analysis of Markov decision processes with Büchi objectives
Formal Methods in System Design
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We present an algorithm that computes in a linear number of symbolic steps (O(|V|)) the strongly connected components (sccs) of a graph G = 〈V, E〉 represented by an Ordered Binary Decision Diagram (OBDD). This result matches the complexity of the (celebrated) Tarjan's algorithm operating on explicit data structures. To date, the best algorithm for the above problem works in Θ(|V|log|V|) symbolic steps ([BGS00]).