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
Graded-CTL: Satisfiability and Symbolic Model Checking
ICFEM '09 Proceedings of the 11th International Conference on Formal Engineering Methods: Formal Methods and Software Engineering
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
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
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
An incremental approach to model checking progress properties
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
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
Priority functions for the approximation of the metric TSP
Information Processing Letters
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The importance of symbolic data structures such as Ordered Binary Decision Diagrams (OBDD) is rapidly growing in many areas of Computer Science where the large dimensions of the input models is a challenging feature: OBDD based graph representations allowed to define truly new standards in the achievable dimensions for the Model Checking verification technique. However, OBDD representations pose strict constraints in the algorithm design issue. For example, Depth-First Search (DFS) is not feasible in a symbolic framework and, consequently, many state-of-the-art DFS based algorithms (e.g., connectivity procedures) cannot be easily rearranged to work on symbolically represented graphs. We devise here a symbolic algorithmic strategy, based on the new notion of spine-set, that is general enough to be the engine of linear symbolic step algorithms for both strongly connected components and biconnected components. Our procedures improve on previously designed connectivity symbolic algorithms. Moreover, by an application to the so-called “bad cycle detection problem”, our technique can be used to efficiently solve the emptiness problem for various kinds of ω-automata.