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Grammar (informal)
A set of rules used to define the structure of the strings in a language TERM 2
Language of a grammar
DEFINITION 2 If G is a grammar with start symbol S and set of terminals T, then the language of G is the set L(G) = {s | s is an element T* and S => + s} If G is a grammar then the language of G is the set of terminal strings derived from the start symbol of G. TERM 3
grammar (formal)
DEFINITION 3
- An alphabet N of grammar symbols called nonterminals 2. An alphabet T of symbols called terminals. The terminals are distinct from the nonterminals. 3. A specific N.T S, called the start symbol
- A finite set of pr.tions of the form a -> B where a and B are strings over the alphabet N U T with the restriction that a is not the empty string. There is at least one pro. with only the start symbol S on its left side. Each NT must appear on the left side of some prd. TERM 4
Nonterminal
DEFINITION 4 uppercase letters, production rules TERM 5
Terminals
DEFINITION 5 Literal strings of input into a grammar denoted by lower case letters
grammars important to CS
for defining programming languages and defining data sets for programs. TERM 7
inductive definition of a
set
DEFINITION 7 Basis: Specify one or more elements of S Induction: Give one or more rules to construct new elements of S from existing elements of S. Closure: State that S consists exactly of the elements obtained by the basis and induction steps. This step is usually assumed. Any language defined by a grammar is an inductively defined set TERM 8
production
DEFINITION 8 the grammar rule a -> B is called a production TERM 9
Derivation step
DEFINITION 9 the process of replacing S by aS (using a production) TERM 10
sentential form
DEFINITION 10 A string made up of terminals and/or nonterminals
4 representations of regular languages
regular expressions, DFAs, NFAs, and regular grammars any regular grammar, or regular language is context free TERM 17
pushdown automaton (informal)
DEFINITION 17 is a finite automaton with a stack, used to recognize context- free languages. TERM 18
3 stack operations associated with
PDA
DEFINITION 18 push -- writes a designated symbol onto the top of the stack pop reads the top symbol and removes it from the stack nop does nothing to the stack TERM 19
final state PDA accept/reject
DEFINITION 19 accepted if there is some path from the start state to a final state that consumes all the letters of the string, otherwise the string is rejected. the language is the set of strings that it accepts TERM 20
nondeterministic/deterministic PDA
DEFINITION 20 if there is at most one move possible from each state it is deterministic. Two types of nondeterministic 1) A state has 2 or more outgoing edges with the same input symbol and same stack symbol 2) A state has 2 outgoing edges with the same top stack symbol and one input symbol is lamda with the other being an alphabet symbol
famous example of irregular
language
{a^nb^n | n >=0} TERM 22
empty-stack acceptance PDA
DEFINITION 22 the input string is consumed and the stack is empty but final state does not matter TERM 23
7 tuple (S, A, B, I, E, s,
F)
DEFINITION 23 (S,A,B,I,E,s,F) S- set of states A - alphabet for input string B - set of stack symbols I - set of instructions E - stack start symbol s - the start state F - set of final states TERM 24
Instantaneous Description (ID) (i, abc, XYZW)
DEFINITION 24 describes the execution work of a PDA (i, abc, XYZW) i - pda current state 'a' - is the current input symbol X - is stack top symbol TERM 25
Can nearly all compiler constructs be
represented by CFGs?
DEFINITION 25 True, generally deterministic PDAs because then you dont have to deal with backtracking
