New Lower Bounds and Hierarchy Results for Restricted Branching Programs

✍ Scribed by Detlef Sieling

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 404 KB
• Volume: 53
• Category: Article
• ISSN: 0022-0000
• DOI: 10.1006/jcss.1996.0050

✦ Synopsis

In unrestricted branching programs all variables may be tested arbitrarily often on each path. But exponential lower bounds are only known if on each path the number of tests of each variable is bounded. We examine branching programs in which for each path the number of variables that are tested more than once is bounded by k but we do not bound the number of tests of those variables. Using a new lower bound method we can prove that such branching programs become more powerful by increasing k only by 1: For k (1&=)(nÂ3) (1Â3) Âlog 2Â3 n, where =>0, we exhibit Boolean functions that can be represented in polynomial size if k variables may be tested more than once on each path, but only in exponential size if k&1 variables may be tested more than once on each path. Therefore, we obtain a tight hierarchy.