55 lines
1.3 KiB
Markdown
55 lines
1.3 KiB
Markdown
---
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type: theoretical
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ty:
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---
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## The foundations of computation
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Looking for answers for basic questions like:
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- Computability?
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- Power $\leftrightarrow$ Programming constructs?
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Which leads us to fundamental concepts like:
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- State
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- Transitions
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- Non-determinism
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- Undecideability
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## Models
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### Finite memory
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Finite automata, regexp
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### Finite memory with stack
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Push down automata
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### Unrestricted
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Turing machines
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## Grammars
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On a higher level, it seems like grammars and machines are very different, but parsing a language (a set of strings) is quite similar to computation.
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## State-based systems and glossary
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An FSM can be a specification for OOP.
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- States ($q_0,\ldots, q_n$)
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- Transitions ($a,b,c,\ldots,z$)
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- We can interpret the transitions as class methods and specify the sequences of allowed invocations - **typestate**
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## Notation
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- $x \in X, X\subseteq Y$
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- $\forall x \in X: P(x), \exists x \in X: P(x)$
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- $R \subseteq X \times Y$ is a relation between $X$ and $Y$
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- $xRy \equiv (x,y) \in R$
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- $G = (V, E)$, where $E \subseteq V\times V$ is a directed graph
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Part of [Relations and Digraphs](Relations%20and%20Digraphs.md) |