An n log n Algorithm for Online BDD Refinement

Binary Decision Diagrams are in widespread use in verification systems for the canonical representation of finite functions. Here we consider multi-valued BDDs, which represent functions of the form \(\varphi :\mathbb{B}^\upsilon \to \mathcal{L}\), where \(\mathcal{L}\) is a finite set of leaves.

[1]  Ingo Wegener,et al.  Reduction of OBDDs in Linear Time , 1993, Inf. Process. Lett..

[2]  Igor Walukiewicz,et al.  Automata for the-calculus and Related Results , 1995 .

[3]  David Lee,et al.  Online minimization of transition systems (extended abstract) , 1992, STOC '92.

[4]  John E. Hopcroft,et al.  An n log n algorithm for minimizing states in a finite automaton , 1971 .

[5]  Norbert Blum,et al.  An O(n log n) Implementation of the Standard Method for Minimizing n-State Finite Automata , 1996, Inf. Process. Lett..

[6]  Peter Bro Miltersen,et al.  Tables Should Be Sorted (On Random Access Machines) , 1995, WADS.

[7]  Chen-Shang Lin,et al.  On the OBDD-Representation of General Boolean Functions , 1992, IEEE Trans. Computers.

[8]  Robert E. Tarjan,et al.  Three Partition Refinement Algorithms , 1987, SIAM J. Comput..

[9]  Maxime Crochemore,et al.  Partitioning a Graph in O(|A| log2 |V|) , 1982, Theoretical Computer Science.

[10]  Aarti Gupta,et al.  Representation and symbolic manipulation of linearly inductive Boolean functions , 1993, ICCAD.

[11]  Li Xuandong,et al.  Compositional model-checking for real-time systems , 1998, SOEN.

[12]  Nils Klarlund,et al.  Hardware Verification using Monadic Second-Order Logic , 1995, CAV.

[13]  Anna Ingólfsdóttir,et al.  A Semantic Theory for Value – Passing Processes Late Approach Part II : A Behavioural Semantics , 1995 .

[14]  Nils Klarlund,et al.  Mona: Monadic Second-Order Logic in Practice , 1995, TACAS.

[15]  Jan Friso Groote,et al.  A Complete Equational Axiomatization for MPA with String Iteration , 1995, Theor. Comput. Sci..

[16]  Nils Klarlund An n log n Algorithm for Online BDD Refinement , 1999, J. Algorithms.

[17]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.