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formal_languages_and_compilers/lesson_01.md

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+# Formal languages and compilers
+##### Luca Oddone Breveglieri
+## Introduction
+
+### What is a formal language?
+
+Contrary to natural language, it is meant to communicate with machines.
+
+A language is *formal* if its *syntax* (structure) and *semantic* (interpretation) are defined in a precise algorithmic way.
+
+There is an effective procedure to verify the grammatical *correctness* of a phrase and determine its meaning.
+
+###### It is a mathematical object composed by:
+- An __alphabet__ and built over a
+    - __grammar__ consisting in axiomatic rules
+    - or an __automata__
+
+### Hystorical notes
+
+##### Years '50
+- Chomsky proposes the mathematical model of a grammar (1956)
+
+##### Years '60
+- Connection between formal languages and automata
+- Invention of formal grammars
+- Development of automated compilation
+
+##### Years '70-'80
+- Formal language theory becomes a standard university discipline
+- Introduction of SDKs like Flex or Bison
+
+## Lesson 1
+### Definition of a language
+- __Alphabet__: finite set of elements
+- __String__: Ordered set of atomic elements, possibly repeated
+- __Language__: Finite or infinite set of __strings__
+
+__Strings__ can be both __finite__ or __infinite__.
+
+The __cardinality__ of a *language* determines the number of elements contained,
+
+It can be 0 for the __empty language__ or *infinite* for __infinite languages__.
+
+### Operations on strings
+
+#### Concatenation (product of strings)
+- Is a basic operation,
+- Is associative,
+- Changes the length.
+
+##### Empty string (or null string) Ɛ:
+ is the neutral element respective to concatenation
+##### Substring:
+Given a string x = u y v
+- x is a prefix
+- y is a substring
+- v is a suffix
+
+if u,v ≠ Ɛ,  y is a proper substring
+##### Mirroring or Reflection
+##### Repetition or iteration
+##### Concatenation

soft_computing/lesson_01.md

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+# Soft Computing
+#### Andrea Bonarini
+##### 5 October 2015
+
+#### What is Soft Computing?
+
+The term was introduced by Lotfi Zadeh, the father of fuzzy sets,
+to denote programming techniques not related to *traditional* programming languages:
+- Fuzzy systems
+- Neural networks
+- Stochastic systems
+
+##### definition
+A set of techniques to model systems (input-output mapping) by approximating them.
+
+##### Modelling technique: generalization
+Considers a small sample of the entity to make an approximate model,
+
+
+#### Model
+
+- Is a *representation* of some entity, defined for a *specific purpose*.
+
+- Is limited to aspects of the entity represented which are *relevant for the purpose*
+
+- A model is different to the represented entity ex: map vs land
+
+- Models lead to *approximation, uncertainty, imprecision*.
+
+##### Approximation
+The model features are similar to the real ones but not the same.
+##### Uncertainty
+We are not sure that the features of the model are the same of the entity.
+##### Imprecision
+The model features values are not precise.
+
+#### Techniques
+
+- ##### Fuzzy sets:
+    Correct model in a finite number of points, smooth transistion (approximation) among them.
+
+    ex: in a thermal control system we fix the normal working point and the critical one, and the system approximates the behaviour between.
+
+- ##### Neural networks
+    input-output samples, learning algorithms to define output values for unknown values.
+
+- ##### Genetic algorithms
+    Optimal solution, obtained by evaluating populations of tentative solutions and combining their parts (sort of copying from nature).
+
+#### Applications:
+
+From washing machines to helicopters, to rice cookers
+
+### Fuzzy Sets
+
+Were created in 1965 by Lotfi Zadeh
+
+The principle is to make computation with words.
+
+#### What is a fuzzy set?
+Is a set whose membership function can range on the interval [0,1].
+
+On contrary to __crisp sets__ that admit only {0,1}
+
+###### A membership function defines a set
+###### Defines the degree of membership of an element to the set
+μ: U -> [0,1]
+
+#### How to define membership functions
+- select a variable
+    - distance
+- define a range of the variable
+    - [0..10]
+- identify labels
+    - close, medium, far
+- for each label identify the charachteristic points
+    - 0, max, middle values, where MF=1, ...
+- identify function shapes
+    - linear
+- check
+
+#### MF and concepts
+
+__MFs__ define __fuzzy sets__
+
+__Labels__ denote __fuzzy sets__
+
+__Fuzzy sets__ can be considered as conceptual representations
+
+#### Symbol grounding
+Reason in terms of concepts and grounds them to reality.