On Synchronized Multitape and Multihead Automata

  • Oscar H. Ibarra
  • Nicholas Q. Tran
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6808)

Abstract

Motivated by applications to verification problems in string manipulating programs, we look at the problem of whether the heads in a multitape automaton are synchronized. Given an n-tape pushdown automaton M with a one-way read-only head per tape and a right end marker $ on each tape, and an integer k ≥ 0, we say that M is k-synchronized if at any time during any computation of M on any input n-tuple (x1, …, xn) (whether or not it is accepted), no pair of input heads that are not on $ are more than k cells apart. This requirement is automatically satisfied if one of the heads has reached $. Note that an n-tuple (x1, …, xn) is accepted if M reaches the configuration where all n heads are on $ and M is in an accepting state. The automaton can be deterministic (DPDA) or nondeterministic (NPDA) and, in the special case, may not have a pushdown stack (DFA, NFA). We obtain decidability and undecidability results for these devices for both one-way and two-way versions. We also consider the notion of k-synchronized one-way and two-way multihead automata and investigate similar problems.

Keywords

multitape automata multihead automata synchronized reversal-bounded counters 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Oscar H. Ibarra
    • 1
  • Nicholas Q. Tran
    • 2
  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of Mathematics & Computer ScienceSanta Clara UniversitySanta ClaraUSA

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