Theory of Computing Systems

, Volume 43, Issue 2, pp 159–184 | Cite as

Incremental Branching Programs



We propose a new model of restricted branching programs specific to solving GEN problems, which we call incremental branching programs. We show that syntactic incremental branching programs capture previously studied models of computation for the problem GEN, namely marking machines (Cook, S.A. in J. Comput. Syst. Sci. 9(3):308–316, 1974) and Poon’s extension (Proc. of the 34th IEEE Symp. on the Foundations of Computer Science, pp. 218–227, 1993) of jumping automata on graphs (Cook, S.A., Rackoff, C.W. in SIAM J. Comput. 9:636–652, 1980). We then prove exponential size lower bounds for our syntactic incremental model, and for some other variants of branching program computation for GEN. We further show that nondeterministic syntactic incremental branching programs are provably stronger than their deterministic counterpart when solving a natural NL-complete GEN sub-problem. It remains open if syntactic incremental branching programs are as powerful as unrestricted branching programs for GEN problems.


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Dept. of Computer ScienceUniversity of Texas at AustinAustinUSA
  2. 2.Institute of MathematicsAcademy of Sciences of the Czech RepublicPragueCzech Republic
  3. 3.Dept. d’Informatique et recherche opérationnelleUniversité de MontréalMontréalCanada

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