Firstpos compiler design

  • .
    1. Step 1: Expression Tree.
      2. Augment r with a special end symbol # to get r#, e.g. (a+b)*abb# .
    2. Step 2: Unique Number for Leaf Nodes.
      3. Assign a unique integer to each leaf node (except for the leaf) of the expression tree.
    3. Step 3: nullable(n), firstpos(n), lastpos(n)
    4. Step 4: followpos(n)
    5. Step 5: Generate DFA

  • How do you find Firstpos and Lastpos?

    The firstpos( ) and the laspos( ) is given by the union of the firstpos and lastpos of its children.
    Hence, it is given by {1,2}.
    The interior node, “.”, which is a parent of * and (3), the firstpos( . ) is computed as union of the firstpos() of its children since c1 being the * node is nullable..

  • How to convert re into DFA?

    Steps To Convert Regular Expressions To Finite Automata
    Step 1: Make a transition diagram for a given regular expression, using NFA with ε moves.
    Step 2: Then, Convert this NFA with ε to NFA without ε.
    Step 3: Finally, Convert the obtained NFA to equivalent DFA..

  • What does a B )* mean?

    So, a+b means [ab] or ab , thus (a+b)* means any string of length 0 or more, containing any number of a s and b s in any order.
    Likewise, (a*b*)* also means any string of length 0 or more, containing any number of a s and b s in any order.
    The two expressions are different ways of expressing the same language..

  • What is Firstpos in compiler design?

    • firstpos(n): set of positions under n that can match the. first symbol of a string in L(n) • lastpos(n): the set of positions under n that can match. the last symbol of a string in L(n) • followpos(i): the set of positions that can follow..

  • What is Firstpos in syntax tree?

    The function firstpos(n) is defined as the set of positions that can match the first symbol of a string generated by the sub-tree at node “n”.
    It is defined for all the nodes and depends on the firstpos() values of the leaf nodes..

  • What is the construction method of DFA?

    Utility – To construct DFA from a given regular expression, we can first construct an NFA for the given expression and then convert this NFA to DFA by a subset construction method.
    But to avoid this two-step procedure, the other way round is to directly construct a DFA for the given expression.Feb 22, 2022.

  • What is the difference between DFA and regular expression?

    A DFA is a recognizer for Chomsky type 3 grammars.
    A regular expression is a representation of the production rules of a Chomsky type 3 grammar.
    They are 100% identical in power and expression..

  • Explanation

    1. Step 1 − q0 is an initial state on input '1' goes to q1 and on input '0' leads to a dead state
    2. Step 2 − q1 on input '0' goes to q2 and on '1' goes to dead state
    3. Step 3 − q2 on input '1' goes to qf which is the final state, and on '0' goes to dead state
  • NFA (Non-Deterministic finite automata) NFA stands for non-deterministic finite automata.
    It is easy to construct an NFA than DFA for a given regular language.
    The finite automata are called NFA when there exist many paths for specific input from the current state to the next state.
  • Utility – To construct DFA from a given regular expression, we can first construct an NFA for the given expression and then convert this NFA to DFA by a subset construction method.
    But to avoid this two-step procedure, the other way round is to directly construct a DFA for the given expression.Feb 22, 2022
Feb 22, 20221. Firstly, we construct the augmented regular expression for the given expression.2. Then we construct the syntax tree for r#.3. Next we 
Feb 22, 20221. If n is a cat-node with left child c1 and right child c2 and i is a position in lastpos(c1), then all positions in firstpos(c2) are in 
Feb 22, 2022The start state of DFA D is firstpos(root) and the accepting states are all those containing the position associated with the endmarker symbol 

How do we compute nullable firstpos and lastpos?

We can compute nullable, firstpos, and lastpos by a straightforward recursion on the height of the tree.
The basis and inductive rules for nullable and firstpos are summarized in Fig. 3.58.
The rules for lastpos are essentially the same as for firstpos, but the roles of children c and c2 must be swapped in the rule for a cat-node.

What is firstpos n 1 3?

firstpos {n) — {1,2,3} .
In a typical generated string like aa, the first position of the string corresponds to position 1 of the tree, and in a string like 6a, the first position of the string comes from position 2 of the tree.
However, when the string generated by the expression of node n is just a, then this a comes from position 3.

What is rule 1 for followpos?

Rule 1 for followpos requires that we look at each cat-node, and put each position in firstpos of its right child in followpos for each position in lastpos of its left child.
For the lowest cat-node in Fig. 3.59, that rule says position 3 is in followpos (l) and followpos {2).

Why is the first algorithm useful in a Lex compiler?

The first algorithm is useful in a Lex compiler, because it constructs a DFA directly from a regular expression, without constructing an interme-diate NFA.
The resulting DFA also may have fewer states than the DFA constructed via an NFA.


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