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Multi-stack-counter languages

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Abstract

A stack-counter acceptor is a stack acceptor in which the storage alphabet is just one letter. The present paper discusses multi-stack-counter acceptors operating in quasirealtime, i.e., acceptors in which each storage tape is a stack counter and in which there are only a bounded number of consecutive∈-moves. For each positive integerk let

be the family of languages accepted byk-stack-counter acceptors (k-counter acceptors). Each

is a principal AFL closed under reversal but not under∈-free substitution or under intersection. Also,

and a specific language in each

, is exhibited. For each

and there are noi andj such that

. It is shown that a quasi-real-timek-stackcounter acceptor is equivalent to one operating in non-deterministic real time. Lastly, it is shown that acceptance by final state of ak-stack-counter acceptor is equivalent to acceptance by empty tape and final state.

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Author information

Authors and Affiliations

  1. Harvard University, Cambridge, Massachusetts, USA

    Ronald Book

  2. University of Southern California, Los Angeles, California, USA

    Seymour Ginsburg

Authors
  1. Ronald Book
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  2. Seymour Ginsburg
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Additional information

Also formerly with System Development Corporation, Santa Monica, California. Research sponsored in part by the Air Force Cambridge Research Laboratories, Office of Aerospace Research, USAF, under Contract F19628-70-C-0023; by the Air Force Office of Scientific Research, Office of Aerospace Research, USAF, under AFOSR No. F44620-70-C-0013; and by NSF Grant No. GJ454.

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Book, R., Ginsburg, S. Multi-stack-counter languages. Math. Systems Theory 6, 37–48 (1972). https://doi.org/10.1007/BF01706072

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  • DOI: https://doi.org/10.1007/BF01706072

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