On synchronized multi-tape and multi-head automata

  • Authors:
  • Oscar H. Ibarra;Nicholas Q. Tran

  • Affiliations:
  • Department of Computer Science, University of California, Santa Barbara, CA 93106, USA;Department of Mathematics & Computer Science, Santa Clara University, Santa Clara, CA 95053, USA

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2012

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Abstract

Motivated by applications to verification problems in string manipulating programs, we look at the problem of whether the heads in a multi-tape 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 (x"1,...,x"n) (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 (x"1,...,x"n) 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 multi-head automata and investigate similar problems.