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 (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 multihead automata and investigate similar problems.
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Ibarra, O.H., Tran, N.Q. (2011). On Synchronized Multitape and Multihead Automata. In: Holzer, M., Kutrib, M., Pighizzini, G. (eds) Descriptional Complexity of Formal Systems. DCFS 2011. Lecture Notes in Computer Science, vol 6808. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22600-7_15
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DOI: https://doi.org/10.1007/978-3-642-22600-7_15
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