Unsimulability, Universality, and Undecidability in the Gizmo Framework
The gizmo framework is a recent development of the gadget framework used for proving computational complexity results of videogames and other motion planning problems. This thesis explores three aspects of the gizmo framework: unsimulability (the inability of one gizmo to simulate another gizmo), un...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2023
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| Online Access: | https://hdl.handle.net/1721.1/150149 |
| _version_ | 1811094492971794432 |
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| author | Ani, Joshua |
| author2 | Demaine, Erik D. |
| author_facet | Demaine, Erik D. Ani, Joshua |
| author_sort | Ani, Joshua |
| collection | MIT |
| description | The gizmo framework is a recent development of the gadget framework used for proving computational complexity results of videogames and other motion planning problems. This thesis explores three aspects of the gizmo framework: unsimulability (the inability of one gizmo to simulate another gizmo), universality (the ability of a gizmo to simulate all gizmos in its simulability class), and undecidability (the inability to decide whether a maze made of a gizmo is solvable). We give a proof that the 1- toggle cannot simulate the 2-toggle, as it contains important techniques. We explore a class of gizmos called dicrumbler variants, and give partial results for which ones simulate which others. We give universal gizmos for simulability classes Reg and DAG, and explore the concept of finding all the gizmos that simulate a particular gizmo, with partial results given for the dicrumbler. We show that reachability for a gizmo representing a counter in a counter machine is undecidable, and show several gizmo simulations. We give a proof that generalized New Super Mario Bros. is undecidable using one of the undecidable gizmos. |
| first_indexed | 2024-09-23T16:01:10Z |
| format | Thesis |
| id | mit-1721.1/150149 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:01:10Z |
| publishDate | 2023 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1501492023-04-01T03:06:00Z Unsimulability, Universality, and Undecidability in the Gizmo Framework Ani, Joshua Demaine, Erik D. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science The gizmo framework is a recent development of the gadget framework used for proving computational complexity results of videogames and other motion planning problems. This thesis explores three aspects of the gizmo framework: unsimulability (the inability of one gizmo to simulate another gizmo), universality (the ability of a gizmo to simulate all gizmos in its simulability class), and undecidability (the inability to decide whether a maze made of a gizmo is solvable). We give a proof that the 1- toggle cannot simulate the 2-toggle, as it contains important techniques. We explore a class of gizmos called dicrumbler variants, and give partial results for which ones simulate which others. We give universal gizmos for simulability classes Reg and DAG, and explore the concept of finding all the gizmos that simulate a particular gizmo, with partial results given for the dicrumbler. We show that reachability for a gizmo representing a counter in a counter machine is undecidable, and show several gizmo simulations. We give a proof that generalized New Super Mario Bros. is undecidable using one of the undecidable gizmos. M.Eng. 2023-03-31T14:35:50Z 2023-03-31T14:35:50Z 2023-02 2023-02-27T18:43:21.420Z Thesis https://hdl.handle.net/1721.1/150149 In Copyright - Educational Use Permitted Copyright MIT http://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Ani, Joshua Unsimulability, Universality, and Undecidability in the Gizmo Framework |
| title | Unsimulability, Universality, and Undecidability in the Gizmo Framework |
| title_full | Unsimulability, Universality, and Undecidability in the Gizmo Framework |
| title_fullStr | Unsimulability, Universality, and Undecidability in the Gizmo Framework |
| title_full_unstemmed | Unsimulability, Universality, and Undecidability in the Gizmo Framework |
| title_short | Unsimulability, Universality, and Undecidability in the Gizmo Framework |
| title_sort | unsimulability universality and undecidability in the gizmo framework |
| url | https://hdl.handle.net/1721.1/150149 |
| work_keys_str_mv | AT anijoshua unsimulabilityuniversalityandundecidabilityinthegizmoframework |