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Computer Science > Formal Languages and Automata Theory

arXiv:2212.03791 (cs)
[Submitted on 7 Dec 2022]

Title:On Families of Full Trios Containing Counter Machine Languages

Authors:Oscar H. Ibarra, Ian McQuillan
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Abstract:We look at nondeterministic finite automata augmented with multiple reversal-bounded counters where, during an accepting computation, the behavior of the counters is specified by some fixed pattern. These patterns can serve as a useful "bridge" to other important automata and grammar models in the theoretical computer science literature, thereby helping in their study. Various pattern behaviors are considered, together with characterizations and comparisons. For example, one such pattern defines exactly the smallest full trio containing all the bounded semilinear languages. Another pattern defines the smallest full trio containing all the bounded context-free languages. The "bridging" to other families is then applied, e.g. to certain Turing machine restrictions, as well as other families. Certain general decidability properties are also studied using this framework.
Comments: 28 pages, 1 figure
Subjects: Formal Languages and Automata Theory (cs.FL)
ACM classes: F.4.3
Cite as: arXiv:2212.03791 [cs.FL]
  (or arXiv:2212.03791v1 [cs.FL] for this version)
  https://doi.org/10.48550/arXiv.2212.03791
Journal reference: Theoretical Computer Science 799, 71--93 (2019)
Related DOI: https://doi.org/10.1016/j.tcs.2019.09.045

Submission history

From: Ian McQuillan [view email]
[v1] Wed, 7 Dec 2022 17:17:02 UTC (685 KB)
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