# A Moderately Exponential Time Algorithm for k-IBDD Satisfiability

A Moderately Exponential Time Algorithm for k-IBDD Satisfiability We present a satisfiability algorithm for k-indexed binary decision diagrams (k-IBDDs). The proposed exponential space and deterministic algorithm solves the satisfiability of k-IBDDs, i.e., k-IBDD SAT, for instances with n variables and cn nodes in $$O\left( 2^{(1-\mu _k(c))n}\right)$$ O 2 ( 1 - μ k ( c ) ) n time, where $$\mu _k(c) = \varOmega \left( \frac{1}{(k^2 2^k\log {c})^{2^{k-1}-1}}\right)$$ μ k ( c ) = Ω 1 ( k 2 2 k log c ) 2 k - 1 - 1 . We also provide a polynomial space and deterministic algorithm that solves a k-IBDD SAT of polynomial size for any constant $$k \ge 2$$ k ≥ 2 in $$O\left( 2^{ n - n^{ 1/2^{k-1} }}\right)$$ O 2 n - n 1 / 2 k - 1 time. In addition, the proposed algorithm is applicable to equivalence checking of two IBDDs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algorithmica Springer Journals

# A Moderately Exponential Time Algorithm for k-IBDD Satisfiability

, Volume 80 (10) – Jun 20, 2017
17 pages

/lp/springer_journal/a-moderately-exponential-time-algorithm-for-k-ibdd-satisfiability-GhTOqR2Gzf
Publisher
Springer Journals
Subject
Computer Science; Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Information Theory
ISSN
0178-4617
eISSN
1432-0541
D.O.I.
10.1007/s00453-017-0332-2
Publisher site
See Article on Publisher Site

### Abstract

We present a satisfiability algorithm for k-indexed binary decision diagrams (k-IBDDs). The proposed exponential space and deterministic algorithm solves the satisfiability of k-IBDDs, i.e., k-IBDD SAT, for instances with n variables and cn nodes in $$O\left( 2^{(1-\mu _k(c))n}\right)$$ O 2 ( 1 - μ k ( c ) ) n time, where $$\mu _k(c) = \varOmega \left( \frac{1}{(k^2 2^k\log {c})^{2^{k-1}-1}}\right)$$ μ k ( c ) = Ω 1 ( k 2 2 k log c ) 2 k - 1 - 1 . We also provide a polynomial space and deterministic algorithm that solves a k-IBDD SAT of polynomial size for any constant $$k \ge 2$$ k ≥ 2 in $$O\left( 2^{ n - n^{ 1/2^{k-1} }}\right)$$ O 2 n - n 1 / 2 k - 1 time. In addition, the proposed algorithm is applicable to equivalence checking of two IBDDs.

### Journal

AlgorithmicaSpringer Journals

Published: Jun 20, 2017

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