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Languages & Machines/Introduction.md

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+---
+type: theoretical
+ty:
+---
+
+## The foundations of computation
+Looking for answers for basic questions like:
+- Computability?
+- Power $\leftrightarrow$ Programming constructs?
+
+Which leads us to fundamental concepts like:
+- State
+- Transitions
+- Non-determinism
+- Undecideability
+
+
+## Models
+### Finite memory
+Finite automata, regexp
+![](Pasted%20image%2020250414190100.png)
+### Finite memory with stack
+Push down automata
+![](Pasted%20image%2020250414190119.png)
+### Unrestricted
+Turing machines
+
+![](Pasted%20image%2020250414190144.png)
+
+
+
+## Grammars
+
+![](Pasted%20image%2020250414190229.png)
+
+
+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.
+
+## State-based systems and glossary
+An FSM can be a specification for OOP.
+
+- States ($q_0,\ldots, q_n$)
+- Transitions ($a,b,c,\ldots,z$)
+- We can interpret the transitions as class methods and specify the sequences of allowed invocations - **typestate**
+
+
+
+## Notation
+- $x \in X, X\subseteq Y$
+- $\forall x \in X: P(x), \exists x \in X: P(x)$
+- $R \subseteq X \times Y$ is a relation between $X$ and $Y$
+- $xRy \equiv (x,y) \in R$ 
+- $G = (V, E)$, where $E \subseteq V\times V$ is a directed graph
+
+Part of [Relations and Digraphs](Relations%20and%20Digraphs.md)