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Related Experiment Video

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Generating Strictly Controlled Stimuli for Figure Recognition Experiments

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Some decision problems for bottom-up triangle acceptors.

¹Department of Applied Mathematics, Hiroshima University, Hiroshima, Japan; Computer Science Center, University of Maryland, College Park, MD 20742.

IEEE Transactions on Pattern Analysis and Machine Intelligence

|August 27, 2011

Summary

This summary is machine-generated.

The emptiness problem for deterministic bottom-up triangle acceptors is unsolvable. This finding also proves the unsolvability of certain decision problems for both triangle and pyramid acceptors.

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Area of Science:

Theoretical Computer Science
Formal Languages and Automata Theory

Background:

Deterministic bottom-up triangle acceptors (BTA's) are a class of automata.
Understanding the decidability of problems related to automata is crucial in theoretical computer science.

Purpose of the Study:

To investigate the decidability of the emptiness problem for deterministic bottom-up triangle acceptors (BTA's).
To extend the findings to other related decision problems concerning BTA's and deterministic bottom-up pyramid acceptors (BPA's).

Main Methods:

Proof by reduction from a known undecidable problem.
Analysis of the computational power and properties of BTA's and BPA's.

Main Results:

The emptiness problem for deterministic bottom-up triangle acceptors (BTA's) over a single input symbol is proven to be recursively unsolvable.
Certain decision problems involving BTA's and deterministic bottom-up pyramid acceptors (BPA's) are also shown to be unsolvable based on the primary result.

Conclusions:

The unsolvability of the emptiness problem for BTA's has significant implications for the theory of computation.
This research highlights fundamental limitations in the decidability of problems for certain classes of automata.