{"id":19975900,"url":"https://github.com/jfjlaros/numauto","last_synced_at":"2025-06-11T21:05:26.882Z","repository":{"id":80229639,"uuid":"123484713","full_name":"jfjlaros/numauto","owner":"jfjlaros","description":"Numeration-automatic sequences.","archived":false,"fork":false,"pushed_at":"2018-03-18T17:50:43.000Z","size":3229,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":2,"default_branch":"master","last_synced_at":"2025-03-01T18:47:10.469Z","etag":null,"topics":["fixed-point","k-automata","number-system","substitutions"],"latest_commit_sha":null,"homepage":"","language":"C","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/jfjlaros.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2018-03-01T19:50:20.000Z","updated_at":"2018-03-18T20:11:02.000Z","dependencies_parsed_at":null,"dependency_job_id":"8b37f9b7-f007-4b86-9cbe-6f585cf32273","html_url":"https://github.com/jfjlaros/numauto","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/jfjlaros/numauto","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/jfjlaros%2Fnumauto","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/jfjlaros%2Fnumauto/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/jfjlaros%2Fnumauto/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/jfjlaros%2Fnumauto/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/jfjlaros","download_url":"https://codeload.github.com/jfjlaros/numauto/tar.gz/refs/heads/master","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/jfjlaros%2Fnumauto/sbom","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":259340515,"owners_count":22843007,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["fixed-point","k-automata","number-system","substitutions"],"created_at":"2024-11-13T03:20:51.640Z","updated_at":"2025-06-11T21:05:26.819Z","avatar_url":"https://github.com/jfjlaros.png","language":"C","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Numeration-automatic sequences\nThis project contains code used in a study of\n[*k*-automata](https://www.fixedpoint.nl/study/dynsys/automata.pdf)\nand\n[numeration-automatic sequences](https://arxiv.org/abs/cs/0605076).\n\n\n## Installation\nRetrieve the source code with Git.\n\n    git clone https://github.com/jfjlaros/numauto.git\n\nCompile the main program.\n\n    cd numauto/src/sequence\n    make\n\n\n## Usage\nThe substitution schema is supplied by entering a list of production rules via\nstandard input. Each production rule has one letter on the left hand side and\none or more letters on the right hand side, the parts are separated by the `\u003e`\nsign.\n\nThe input can be supplied while the program is running. Press `Control-d` when\nthe substitution schema is fully entered.\n\n    ./sequence\n\nAlternatively, the substitution schema can be supplied beforehand and piped\ninto the program as follows:\n\n    cat \u003c\u003c EOF | ./sequence\n    a\u003eabc\n    b\u003eaac\n    c\u003ea\n    EOF\n\nThe output for the example given above, will look like this:\n\n```\nThe matrix:\n1 2 1 \n1 0 0 \n1 1 0 \n\nk = 3\n\nThe fixed point:\nabcaacaabcabcaabcabcaacaabcaacaabcabcaacaabcaacaabcabcaabcabcaacaabcabcaabcabcaa\ncaabcaacaabcabcaabcabcaacaabcabcaabcabcaacaabcaacaabcabcaacaabcaacaabcabcaabcabc\naacaabcaacaabcabcaacaabcaacaabcabcaabcabcaacaabcabcaabcabcaacaabcaacaabcabcaacaa\nbcaacaabcabcaabcabcaacaabcaacaabcabcaacaabcaacaabcabcaabcabcaacaabcabcaabcabcaac\naabcaacaabcabcaabcabcaacaabcabcaabcabcaacaabcaacaabcabcaacaabcaacaabcabcaabcabca\nacaabcabcaabcabcaacaabcaacaabcabcaabcabcaacaabcabcaabcabcaacaabcaacaabcabcaacaab\ncaacaabcabcaabcabcaacaabcaacaabcabcaacaabcaacaabcabcaabcabcaacaabcabcaabcabcaaca\nabcaacaabcabcaabcabcaacaabcabcaabcabcaacaabcaacaabcabcaacaabcaacaabcabcaabcabcaa\ncaabcabcaabcabcaacaabcaacaabcabcaabcabcaacaabcabcaabcabcaacaabcaacaabcabcaacaabc\naacaabcabcaabcabcaacaabcaacaabcabcaacaabcaacaabcabcaabcabcaacaabcabcaabcabcaacaa\nbcaacaabcabcaacaabcaacaabcabcaabcabcaacaabcaacaabcabcaacaabcaacaabcabcaabcabcaac\naabcabcaabcabcaacaabcaacaabcabcaabcabcaacaabcabcaabcabcaacaabcaacaabcabcaacaabca\nacaabcabcaabcabcaacaabcaacaabcabcaacaabcaacaabcabcaabcabcaacaabcabcaabcabcaacaab\ncaacaabcabcaacaabcaacaabcabcaabcabcaacaabcaacaabcabcaacaabcaacaabcabcaabcabcaaca\nabcabcaabcabcaacaabcaacaabcabcaabcabcaacaabcabcaabcabcaacaabcaacaabcabcaacaabcaa\ncaabcabcaabcabcaacaabcabcaabcabcaacaabcaacaabcabcaabcabcaacaabcabcaabcabcaacaabc\n\nThe numeration system:\n1 3 7 17 41 99 239 577\n```\n\nThe following sections of the [paper](https://arxiv.org/abs/cs/0605076) are\nparticularly relevant for the interpretation of the results:\n\n- Section 5: conversion from a substitution to `The matrix`.\n- Definition 2.0.7: `k` in this context.\n- Definition 2.0.6: `The fixed point`.\n- Definition 2.0.8: `The numeration system`.\n\n\n## Additional programs\nThis project contains some additional code that was used during the study. Most\nof the functionality is present in the main program described above.\n\n- A programming library for [*k*-automata](src/k_autom) including examples.\n- A programming library for [Fibonacci automaton](src/fib_autom) including\n  examples.\n- An implementation of substitutions in [general](src/subst) which can be used\n  to verify the correctness of the constructed automata.\n\n\n## Related work\nSome new insights gained during the study were shared with the\n[On-Line Encyclopedia of Integer Sequences](http://oeis.org/):\n\n- The Fibonacci sequence ([A000045](http://oeis.org/A000045)).\n- Other sequences: [A101399](http://oeis.org/A101399),\n  [A101400](http://oeis.org/A101400), [A101169](http://oeis.org/A101169),\n  [A101197](http://oeis.org/A101197), [A101168](http://oeis.org/A101168).\n\n\n## Acknowledgements\nThe author would like to thank Prof.dr. Robert Tijdeman and Dr. Hendrik Jan\nHoogeboom for their numerous comments and insightful ideas.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjfjlaros%2Fnumauto","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fjfjlaros%2Fnumauto","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fjfjlaros%2Fnumauto/lists"}