SolutionComputation of FIRSTS → L = R∵ L does not derive ε. By rule (4b)of FIRST∴ FIRST(S) = {FIRST(L)}                                                  (1)S → R∵ R does not derive ε. By rule (4b)of FIRST∴ FIRST(S) = {FIRST(R)}                                                 (2)L →* RApplying Rule (3) of FIRSTFIRST(L) = {*}                   ... Read More

The LR (0) item for Grammar G consists of a production in which symbol dot (.) is inserted at some position in R.H.S of production.For Example − For the production S → ABC, the generated LR (0) items will be −S →∙ ABCS → A ∙ BCS → AB ∙ CS → ABC ∙Production S → ε generates only one item, i.e., S →∙Canonical LR (0) collection helps to construct LR parser called Simple LR (SLR) parser.To create Canonical LR (0) collection for Grammar, 3 things are required −Augmented GrammarClosure Functiongoto FunctionAugmented Grammar − If grammar G has start symbol ... Read More

LR Parser is a class of Bottom-Up Parser that is used to parse Context-Free Grammars. LR Parsing is known as LR (K) parsing whereL represents Left to Right Scanning of InputR represents Rightmost DerivationK is the number of input symbols of Look ahead that are used in developing parsing decisions.LR parser is a shift-reduce parser that creates the use of deterministic finite automata, identifying the collection of all applicable prefixes by reading the stack from bottom to top.It decides what handle, if any, is feasible. An achievable prefix of a right sentential form is that prefix that includes a handle, ... Read More

Top-Down Parsing with BacktrackingIn Top-Down Parsing with Backtracking, Parser will attempt multiple rules or production to discover the match for input string by backtracking at every step of derivation. So, if the used production does not give the input string as needed, or it does not match with the needed string, then it can undo that shift.Top-Down Parsing without BacktrackingAs backtracking looks more powerful by which we can select different alternatives. But backtracking cannot be applied or implemented so easily in parsing. There are two types of Top-Down Parsing without Backtracking, which are as follows −Recursive Descent ParserPredictive ParserRecursive Descent ... Read More

SolutionComputation of FIRSTE →TE′Applying Rule (4b) of FIRSTSince FIRST (T) does not contain ε, or T does not derive ε.∴ FIRST (E) = FIRST(TE′) = FIRST(T)∴ FIRST (E) = {FIRST(T)} (1)E → +TE′|εApplying Rule (3) of FIRSTComparing E′ → +TE′with X → aα∴ FIRST(E′) = {+}Apply Rule (2) on E′ → εFIRST (E′) = {ε}∴ FIRST(E′) = {+, ε} (2)T→FT′Apply rule (4b) of FIRSTSince, FIRST(F) does not derive ε∴ FIRST(T) = FIRST(FT′) = FIRST(F)∴ FIRST(T) = {FIRST(F)} (3)T′→*FT′|εComparing with rule (2) & (3) of FIRST, we get∴ FIRST(T′) = {ε, ∗} (4)F→(E)|idComparing with rule (3) of FIRST∴ FIRST(F) = {(, ... Read More

Problem − Consider the following grammar − E → TE′ E′ → +TE′|ε T′ → FT′ T′ → FT′|ε F → (E)|id Solution − Step1− Elimination of Left Recursion & perform Left Factoring As there is no left recursion in Grammar so, we will proceed as it is. Also, there is no need for Left Factoring. Step2− Computation of FIRST FIRST(E) = FIRST(T) = FIRST(F) = {(, id} FIRST (E′) = {+, ε} FIRST (T′) = {*, ε} Step3− Computation of FOLLOW FOLLOW (E) = FOLLOW(E′) = {), $} FOLLOW (T) = FOLLOW(T′) = {+, ), $} FOLLOW (F) = ... Read More

SolutionComputation of FIRSTA → b B∴ FIRST(A) = {b}B → ε∴ FIRST(B) = {ε}S → A a AApplying Rule (4) of FIRSTi.e., Comparing S → A a A with X → Y1Y2Y3∴ FIRST (S) = FIRST (A a A) = FIRST (A) = {b}∴ FIRST(S) = {b}S → B b B∵ FIRST (B)contains ε or B derives ε ∴ Applying Rule (4c)∴ FIRST (S) = FIRST (B to B)∴ FIRST (S) = FIRST (B) − {ε} ∪ FIRST(bB)∴ FIRST (S) = FIRST (B) − {ε} ∪ {b} = {ε} − {ε} ∪ {b} = {b}∴ FIRST (A) = {b}FIRST (B) ... Read More

FIRST and FOLLOW are two functions associated with grammar that help us fill in the entries of an M-table.FIRST ()− It is a function that gives the set of terminals that begin the strings derived from the production rule.A symbol c is in FIRST (α) if and only if α ⇒ cβ for some sequence β of grammar symbols.A terminal symbol a is in FOLLOW (N) if and only if there is a derivation from the start symbol S of the grammar such that S ⇒ αNαβ, where α and β are a (possible empty) sequence of grammar symbols. In ... Read More

Predictive Parser is also another method that implements the technique of Top- Down parsing without Backtracking. A predictive parser is an effective technique of executing recursive-descent parsing by managing the stack of activation records, particularly.Predictive Parsers has the following components −Input Buffer − The input buffer includes the string to be parsed followed by an end marker $ to denote the end of the string.Here a, +, b are terminal symbols.Stack − It contains a combination of grammar symbols with $ on the bottom of the stack. At the start of Parsing, the stack contains the start symbol of Grammar ... Read More

Recursive Descent Parser uses the technique of Top-Down Parsing without backtracking. It can be defined as a Parser that uses the various recursive procedure to process the input string with no backtracking. It can be simply performed using a Recursive language. The first symbol of the string of R.H.S of production will uniquely determine the correct alternative to choose.The major approach of recursive-descent parsing is to relate each non-terminal with a procedure. The objective of each procedure is to read a sequence of input characters that can be produced by the corresponding non-terminal, and return a pointer to the root ... Read More