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      Äquivalenzrelation als Pfeildiagramm und als Äquivalenzklassen

      eevvoor · pubsub.movim.eu / dags · Saturday, 17 October, 2020 - 20:52 edit

    https://upload.movim.eu/files/ff2b1221aa0311b7e7441a5f06506d7f0b23b7a8/0SQbDpaYnzE8IUzREHtek2uuVBLH1Ax3jqf268kD/equiv.png

    Menge von acht Buchexemplaren mit eingezeichneter Äquivalenzrelation „a und b besitzen dieselbe ISBN“ als Pfeildiagramm und den Äquivalenzklassen

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      Overview Pic Algebraic Structures

      eevvoor · pubsub.movim.eu / dags · Saturday, 17 October, 2020 - 20:44 edit

    https://upload.movim.eu/files/ff2b1221aa0311b7e7441a5f06506d7f0b23b7a8/uIxVNAE4IUAGu7qiwtMlul8ForcuNJJwCcTLpoG3/alg-struct.png

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      eevvoor · pubsub.movim.eu / dags · Saturday, 17 October, 2020 - 20:42

      Contact publication

    Kongruenzrelation
    • Kongruenzrelation

      In der Mathematik, genauer der Algebra, nennt man eine Äquivalenzrelation auf einer algebraischen Struktur eine Kongruenzrelation, wenn die fundamentalen Operationen der algebraischen Struktur mit dieser Äquivalenzrelation verträglich sind. Definitionen Kongruenzrelation und Quotientenalgebra Eine Äquivalenzrelation auf einer Menge A {\displaystyle A} hat nicht notwendigerweise etwas mit der Struktur zu tun, die darauf definiert ist. Speziell in der Algebra sind jedoch solche Äquivalenzrelationen ≡ …

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      Congruence

      eevvoor · pubsub.movim.eu / dags · Saturday, 17 October, 2020 - 20:25

    In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements.

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      DAG language 𝜆 ⭠r⭢ qq, qq⭠l⭢ 𝜆

      eevvoor · pubsub.movim.eu / dags · Friday, 16 October, 2020 - 17:55 edit

    https://upload.movim.eu/files/ff2b1221aa0311b7e7441a5f06506d7f0b23b7a8/NtG0zWFExBWjYwIxQBOyn0NwRNI9ctPk7Qdf5MGq/drawing.jpg

    With the two rules below, a DAG automaton can pump to have an infinite number of DAGs in its language. The picture shows three of those DAGs. The last one can be accomplished by swapping edges of the first two DAGs.

    • 𝜆 ⭠r⭢ qq
    • qq⭠l⭢ 𝜆
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      Myhill-Nerode Equivalence Relation for DAG-automata

      eevvoor · pubsub.movim.eu / dags · Friday, 16 October, 2020 - 15:00 edit

    The Myhill-Nerode equivalence relation was initially used for string languages. This equivalence is an open problem for DAG languages.

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      Directed Acyclic Graphs -- DAGs

      eevvoor · pubsub.movim.eu / dags · Friday, 16 October, 2020 - 14:46 edit

    https://upload.movim.eu/files/ff2b1221aa0311b7e7441a5f06506d7f0b23b7a8/CKwk9H5raLw8Oxk9rTiT4FQVIcWOu3EwowxddK3U/drawing.jpg

    This is my jotter for drafting and sketching stuff about DAGs and DAG automata.

    We can say "Hi!" with five connected DAGs or one unconnected DAG.

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