Information content in formal languages
| Autor: | Burgstaller, Bernhard |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Motivated by creating physical theories, formal languages $S$ with variables are considered and a kind of distance between elements of the languages is defined by the formula $d(x,y)= \ell(x \nabla y) - \ell(x) \wedge \ell(y)$, where $\ell$ is a length function and $x \nabla y$ means the united theory of $x$ and $y$. Actually we mainly consider abstract abelian idempotent monoids $(S,\nabla)$ provided with length functions $\ell$. The set of length functions can be projected to another set of length functions such that the distance $d$ is actually a pseudometric and satisfies $d(x\nabla a,y\nabla b) \le d(x,y) + d(a,b)$. We also propose a "signed measure" on the set of Boolean expressions of elements in $S$, and a Banach-Mazur-like distance between abelian, idempotent monoids with length functions, or formal languages. Comment: Content is completely unchanged, but explanatory text is inserted between lemmas, theorems and proofs for better understandability of the paper |
| Databáze: | arXiv |
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