Every regular expression describes regular language Automata Theory by ComputeNow - July 27, 2019July 27, 20190 Every regular expression describes regular language, let R be an arbitrary regular expression over the alphabet Σ. We will prove that the language described by R is a regular language. The proof is by induction on the structure of R. The first base case of induction: Assume that R = ε. The R describes the language of {ε}. In order
Turing Machine Definition Automata Theory by ComputeNow - December 22, 2018December 22, 20180 Definition of a Turing Machine We start with an informal description of a Turing Machine. Such a machine consists of the following: There are k tapes , for some fixed k ≥ 1. Each tape is divided into cells, and is infinite both to the left and to the right. Each cell stores a symbol belonging to a
Context Sensitive Grammar and Linear Bounded Automata Automata Theory by ComputeNow - September 21, 20180 A context sensitive grammar (CSG) is a grammar where all productions are of the form αAβ → αγβ where γ ≠ ε. During derivation non-terminal A will be changed to γ only when it is present in the context of α and β. *Note the constraint that the replacement string γ ≠ ε ; as a consequence we have α ⇒ β implies |α| ≤ |β| CSG is a Noncontracting grammar. Formal
Regular Language in Automata Thoery Automata Theory by ComputeNow - September 20, 2018September 18, 20180 Regular Languages or Formal Language : A language is regular if it can be expressed in terms of regular expression. Closure Properties of Regular Languages Union : If L1 and If L2 are two regular languages, their union L1 ∪ L2 will also be regular. For example, L1 = {an | n ≥ 0} and
What is Chomsky Hierarchy in Theory of Computation Automata Theory by ComputeNow - September 19, 2018September 19, 20180 What is Chomsky Hierarchy? Noam Chomsky categorised regular and other languages which called as Chomsky Hierarchy. Language Class Grammar Automaton 3 Regular NFA or DFA 2 Context-Free Push-Down Automaton 1 Context-Sensitive Linear-Bounded Automaton 0 Unrestricted (or Free) Turing Machine This is a hierarchy, so every language of type 3 is also of types 2, 1 and 0; every language of type 2 is also of types 1 and 0
The Pumping Lemma for Context-Free Languages Automata Theory by ComputeNow - September 10, 2018September 10, 20180 The Pumping Lemma for Context-Free Languages (CFL) Proving that something is not a context-free language requires either finding a context-free grammar to describe the language or using another proof technique (though the pumping lemma is the most commonly used one). A common lemma to use to prove that a language is
Context Free Languages Automata Theory by ComputeNow - September 6, 2018September 6, 20180 Context-free languages (CFLs) are generated by context-free grammars. The set of all context-free languages is identical to the set of languages accepted by pushdown automata, and the set of regular languages is a subset of context-free languages. An inputed language is accepted by a computational model if it runs through the model and ends in an accepting final
Regular Expressions – (Regex) – Regular Expression Automata Theory by ComputeNow - September 2, 2018September 2, 20180 Regular Expressions was initially a term borrowed from automata theory in theoretical computer science. Broadly, it refers to patterns to which a sub-string needs to be matched. The comic should have already given you an idea of what regular expressions could be useful for. It should not be surprising that many programming languages, text processing
Context Free Grammars Automata Theory by ComputeNow - August 23, 2018August 23, 20180 Context free grammars (CFGs) are used to describe context-free languages. A context-free grammar is a set of recursive rules used to generate patterns of strings. A context-free grammar can describe all regular languages and more, but they cannot describe all possible languages. Context-free grammars are studied in fields of theoretical computer science, compiler design, and linguistics. CFG’s are
Translating Between Context-Free Grammars and Pushdown Automata Automata Theory by ComputeNow - August 19, 2018August 19, 20180 Context-free Grammar to Pushdown Automata Each derivation or sequence of production rules that results in a given string is made up of intermediate strings (which are made at each step of the derivation). The pushdown automata's nondeterminism helps it to guess the sequence of steps in the derivation that will result in the desired
