Theory of computation ic-2k20-13 Anushka joshi viii semester

[Audio] Hello and welcome to this presentation on formal languages and grammars..

[Audio] Today we will explore various aspects of language structure, including a subset of English grammar, postfix notation, grammar, extended Backus-naur form, BNF, and examples with derivations..

[Audio] Let's start with the rules for constructing valid sentences. Sentences must have a subject and a predicate, both agreeing in number and tense. Proper punctuation, including capitalization at the beginning and appropriate punctuation the at the end, is crucial. Additionally sentences should be grammatically correct and coherent. We then delve into a subset of English grammar covering noun phrases, NP verb phrases, VP, and prepositional phrases p p. For instance a sentence consists of a noun phrase followed by an intransitive verb phrase and another noun phrase. Valid sentences. Examples. We illustrate these rules with examples of valid sentences like John runs, the cat jumps, and the book is on the table.

[Audio] Question one validation of sentences. We proceed to validate sentences using a set of productions. For example, the happy hare runs is broken down into a noun phrase, intransitive verb phrase, and another noun phrase each following specific grammar rules..

[Audio] In postfix notation, also known as reverse Polish notation (RPN), operators are placed after their operands. To evaluate expressions, you can use a stack to keep track of the operands. Here are some examples:1. *Addition*: - Expression: 45+ - Derivation: - Push 4 onto the stack: 4 - Push 5 onto the stack: 4, 5 - Pop 5 and 4, add them, and push the result (9) onto the stack: 9 - Result: 92. *Subtraction*: - Expression: 83- - Derivation: - Push 8 onto the stack: 8 - Push 3 onto the stack: 8, 3 - Pop 3 and 8, subtract 3 from 8, and push the result (5) onto the stack: 5 - Result: 53. *Multiplication*: - Expression: 26* - Derivation: - Push 2 onto the stack: 2 - Push 6 onto the stack: 2, 6 - Pop 6 and 2, multiply them, and push the result (12) onto the stack: 12 - Result: 124. *Division*: - Expression: 102/ - Derivation: - Push 1 onto the stack: 1 - Push 0 onto the stack: 1, 0 - Push 2 onto the stack: 1, 0, 2 - Pop 2 and 0, divide 2 by 0, and push the result (infinity or an error) onto the stack: ∞ or error - Result: ∞ or errorIn these examples, the stack is used to hold operands until an operator is encountered. The operator then operates on the top operands on the stack, and the result is pushed back onto the stack for further operations..

[Audio] Question two derivation trees. To visually represent the process of generating sentences, we construct derivation trees. These trees show step by step production rules for sentences. Let's.

[Audio] create derivation trees for sentences like the tortoise passes the hare..

[Audio] This EBNF grammar defines a signed decimal number as an optional sign followed by one or more digits. The sign can be either '+' or '-', and a digit is any decimal digit from 0 to 9.Valid examples of signed decimal numbers:- +123- -456- 789Invalid examples:- 12.34 (contains a decimal point)- audio script for PPT slide (contains non-digit characters).

[Audio] Question three phrase structure grammar. Moving on we introduce phrase structure grammar, a formal grammar describing language structure. We implement a phrase structure grammar for signed decimal numbers using code, segments and parser. Question three constructing a phrase structure grammar.

[Audio] More on phrase structure grammar examples. Expanding our exploration,.

[Audio] Question four extended Backus-naur form BNF. Next we introduce extended Backus-naur form BNF, a notation allowing optional elements, repetitions, and more. We present production rules for decimal numerals in BNF.

[Audio] We define the grammar rules for signed decimal numbers in backus-naur form BNF and illustrate it. The rules cover signs, non-negative integers, decimal fractions, and positive integers..

[Audio] we provide production rules in BNF for different identifier scenarios, including lowercase letters, uppercase letters, and combinations with digits and underscores..

[Audio] e BNF. For C programming language identifiers, we extend our e BNF exploration to cover identifiers in the C programming language, incorporating variations like starting with a letter or an underscore, and including alphanumeric characters. Postfix notation..

[Audio] extended Backus-naur form BNF. Next we introduce extended Backus-naur form BNF, a notation allowing optional elements, repetitions, and more. We present production rules for decimal numerals in BNF specifying optional sign, non-negative integer, and decimal fraction..

[Audio] postfix notation, an alternative to infix notation in postfix notation, operators.

[Audio] come after operands, contrasting with traditional infix notation used in mathematics and programming languages. Question six postfix notation. Examples. We then analyze strings in postfix notation, determining if they are generated by the provided grammar..

[Audio] We illustrate steps used to generate or not generate strings like ABC plus and XYZ. Question seven infix notation with BNF. Exploring infix notation, we describe its syntax using backus-naur form. BNF..

e) ⟨expression⟩ ⟨term⟩ ⟨factor⟩⟨factor⟩⟨muloperator⟩ ⟨factor⟩⟨expression⟩⟨muloperator⟩ ⟨factor⟩⟨term⟩⟨term⟩⟨addoperator⟩⟨muloperator⟩ ⟨factor⟩⟨factor⟩⟨factor⟩⟨addoperator⟩⟨muloperator⟩ ⟨identifier⟩⟨identifier⟩⟨identifier⟩⟨addoperator⟩⟨muloperator⟩ a d e − ∗ b) not generated.

[Audio] contrasting with traditional infix notation used in mathematics and programming languages..

[Audio] We illustrate steps used to generate or not generate strings like ABC plus and XYZ. Question seven infix notation with BNF. Exploring infix.

[Audio] automata construction In transitioning to automata, we construct a finite automaton for a pushdown automaton,.

[Audio] PDA and a Turing machine TM to accept specific language sets. We also verify strings against these automata..

[Audio] Turing machine. For language O one plus ten. We design a Turing machine to accept strings in the language O1C plus ten,.

[Audio] showcasing the steps taken by the machine in processing an input.

[Audio] PDA for CFG. Finally, we build a pushdown automaton PDA equivalent to a given context free grammar cfg..

[Audio] We test the PDA against a specific string to determine its acceptance..

[Audio] Conclusion and thank you. Thank you for joining us on this journey through formal languages and grammars. If you have any questions or would like further clarification, please feel free to reach out. We appreciate your time and attention..