2023 Fiscal Year Research-status Report
Non-regular complexity theory
| Project/Area Number |
23K10976
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| Research Institution | Akita University |
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Principal Investigator |
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| Project Period (FY) |
2023-04-01 – 2026-03-31
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| Keywords | automata / complexity / regularity |
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| Outline of Annual Research Achievements |
In the first year the project advanced on two fronts:
1. We defined a machine model called freezing 1-tag systems with states. Each symbol may be rewritten to another before the head moves one position to the right and each position may be rewritten only to a symbol that is smaller than the current one in a previously fixed ordering of the alphabet (freezing property). Such models are strictly stronger than finite automata, but the languages accepted are all in DTIME(n^2), so the model is at the low end of computational power. We proved separation results with respect to the classes of the Chomsky-hierarchy and showed that the model is capable of checking some surprising properties that generally require nondeterministic computations in other models.
2. We continued the study of sweep complexity of OWJFA by proving and disproving several conjectures from [Fazekas, Mercas, Wu, 2022, JALC]. We showed that there is no upper bound on machines accepting regular languages in terms of sweep complexity, as there are logarithmic and even linear complexity OWJFA accepting regular languages. We also exhibited OWJFA with logarithmic complexity accepting a non-regular language. Proving non-regularity was achieved by showing that such machines can check logarithmic/exponential relationships between the lengths of certain factors in the input, a very surprising development given that OWJFA do not have access to additional storage.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
As originally planned, in the first year we focused on establishing complexity results in some existing models and introduced new ones, with the longer term goal of obtaining an intuition for possible generalizations.
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| Strategy for Future Research Activity |
The plan for the upcoming year is to investigate related complexity measures in other automata models, as well as some algorithmic properties of these models accepting non-regular languages.
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| Causes of Carryover |
The small amount remaining to be used in the next fiscal year will be added to the travel expenses planned for FY 2024.
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