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A method of generating strings from a CFG starting from the leftmost symbol

One non-terminal leads to only one non-terminal

Unwanted branches do not lead to the required word

Intersection includes words present in both languages, while union includes words from at least one language

Concatenation of finite letters from an alphabet

A string with no symbols, denoted by Lambda, that represents an empty sequence

A word follows language rules, whereas a string is a finite sequence of symbols

The collection of all strings over an alphabet, including the empty string and all concatenations of the alphabet

Because the palindrome definition requires that the reverse of a string equals itself

Specify basic objects, define initial objects if necessary, define each object in terms of other objects

aaa + aab + aba + abb + baa + bab + bba + bbb

((a+b)(a+b))*

(a + b)*

TG's can change state without an input (Null transition), providing more freedom but needing more memory and processing power.

A Finite automaton is a collection of finite number of states, with one initial and possibly some final states, a finite set of input letters, and transitions for each state and input letter showing how to move between states.

FA transitions are deterministic with one transition per letter per state, while NFA's transitions can have more than one transition per letter per state.

In NFA, the next state of the machine and current input do not uniquely determine the next state, allowing for multiple possible subsequent states.

NFA provides a more relaxed structure and it is easier to represent a language using NFA, allowing for the use of methods to convert NFA into FA to simplify representation.

Introduce a new state connected to the original start state with the same transitions, designating the new state as initial and final to accurately accept the null string.

The union of two FA's accepts strings accepted by either FA, concatenation accepts strings where the first part is accepted by the first FA and the second part by the second FA, and closure accepts all strings of the first FA including the empty string.

Moore & Mealy Machines work as incrementing machine & 1's complement machine in computing, providing basic computer operations.

A sequential circuit contains a memory component that provides a state input, often using flip-flops to indicate states and transitions based on inputs.

Pumping Lemma I and II are used to recognize non-regular languages, with PLII having stricter conditions than PLI. PLI requires generating all words of a language to prove non-regularity, while PLII needs only a single word.

Pumping Lemma II is significant as it can prove certain infinite non-regular languages, like PALINDROME, non-regular by easily showing the non-acceptance of certain words.

A word consists of complete combinations of terminals, while a semiword includes terminals concatenated with exactly one nonterminal on the right.

Grammatical rules and regulations

Intersection accepts strings accepted by both FA's independently, while concatenation accepts strings where the first part is accepted by the first FA and the remaining part by the second FA.

There is no difference between the union of two FA's (FA1 U FA2) and the addition of them (FA + FA2), as both operations represent the combination of the languages of the FA's.

All strings ending in 'a'

The first phase of the compiler that recognizes basic language units called tokens

Strings that follow the rules of the language

A tabular representation of a function that takes two arguments and returns a value

Transfer of a letter from one state to another after being read

A string having no letter

(r - 1)'s complement of a number N in base r is rn - r - m - N

A component that holds input for some time and forwards it

Languages determined by regular expressions are regular; otherwise, they are non-regular

A nondeterministic finite state automaton where the next state is not uniquely determined by current state and input

NFA allows various moves and multiple next states; FA has unique transitions with no choices

A string is any combination of the letters of an alphabet whereas the words of a language are the strings that are always made according to certain rules used to define that language.

A word consists of only terminals, while a semiword contains a terminal concatenated with exactly one nonterminal on the right

A derivation tree shows the derivation of a specific word of the language, while a total tree shows all words of the language

An Alphabet is a set in itself. The elements of an Alphabet are called letters.

The string with zero occurrences of symbols (letters) from an alphabet. It is denoted by (Small Greek letter Lambda) or (Capital Greek letter Lambda), is called an empty string or null string.

Practice and familiarity with production rules help in removing ambiguity

Null production produces empty string, while nullable production can lead to empty string through derivation; To handle, delete null productions and add appropriate new productions

The language consisting of (Null String) and the strings s defined over an Alphabet such that Rev(s)=s.

Valid alphabets consist of more than one symbol where no letter is the prefix of another letter of the same alphabet. Invalid alphabets have letters that start with or end in other letters of the same alphabet.

The Pumping Lemma is a theorem to verify the regularity of infinite languages; It ensures that regular languages exhibit loops

ALGOL (ALGOrithmic Language) is one of several high-level languages designed specifically for programming scientific computations.

Sequencing operators are operators that match elements in sequence, such as 'a >> b', 'a && b', and 'a || b'.

Determinism means that a machine knows what to do for every possible input, while Non-Determinism means the machine may or may not know what to do on all possible inputs.

FA's that accept the same set of languages are called Equivalent FA's.

Palindromes are words of a language where the reverse function returns the same string. Reverse function simply reverses a string.

Given an Alphabet, the Kleene Star Closure, denoted by *, is the collection of all strings defined over the alphabet, including the empty string.

Any alphabet is valid if none of its letters appear at the start of any other letter. Otherwise, it is invalid.

The reverse of a string means to write the string in reverse order. This operation does not change the alphabet.

Kleene Star Closure includes the empty string, while PLUS operation does not generate the empty string automatically.

Regular Expression is the generalized form of any regular language through which you can construct any string related to that language.

FA (Finite Automaton) is a finite state machine that recognizes a regular language.

Taking the union of two FA's means the resulting FA should accept all the words accepted by the two FA's individually.

TG has letter transitions for the strings, while GTG has whole regular expressions as transitions between states.

There is no fixed formula to generate Regular Expressions. It is based on the specific language and patterns.

Yes, for both infix and postfix expressions

PDA is an enhancement in FAs where memory is attached to the machine. It is used in advanced electronic machines such as computers.

There is no difference. Both terms describe the memory structure attached with FAs to store characters.

In CNF, if null is part of the language, it is not included. This is the main change a language undergoes in CNF. FAs are drawn without affecting the language when null is part of it.

In CNF, null is not part of the language. The only change in CNF is excluding null. When building a PDA from CFG, the language remains the same as the original CFG.

PDA consists of input letters, input tape, stack characters, a pushdown stack, start state, accept and reject states, push state, pop state, and read state.

Automata theory helps in studying abstract computing devices and what is computable using an abstract machine. It is fundamental for creating compilers, programming languages, and analyzing new computing devices.

Rules for forming words vary for different languages. Strings must adhere to the defined rules of the language. For example, even and odd length strings have different valid and invalid word patterns.

Palindromes of even length are symmetric about the middle line, while palindromes of odd length are symmetric about the middle letter. Palindromes of length 2n and 2n-1 depend on the alphabet used.

Regular expressions for a specific number of words can be written using the alphabet of the language. Example: (a+b)3 represents all possible strings with the length of 3, where 'a' and 'b' are the alphabet characters.

Capital letters are used for convenience when representing languages. Yes, two languages can be combined by using operations like union, intersection, etc.

Rules include defining languages for single letters, product of two languages, union of sets, and Kleene closure. These rules establish a language associated with each regular expression.

Even-Even language refers to strings where the counts of 'a's and 'b's are both even. It can be divided into substrings of length 2 each.

Tokenize a string means make its valid units.

Whole star of any regular expression means all possible combinations of that regular expression, including empty string.

Plus operation is similar to Kleene Star Closure, but it does not generate a null string automatically.

Null string is used in FA if it is part of the language, but it is not compulsory to include.

(a, b) represents the combination of a and b, while (a + b) represents either a or b

(a + b)+ means repeat the expression one or more times, while (a + b)* means repeat the expression zero or more times

The length of a string indicates the number of symbols in that string.

False

FA = Finite Automata with unique transitions TG = Generalization of FA with additional features GTG = Directed edges labeled with regular expressions

Language of strings with substring 00 or 11 in them at least. Minimum words included in this language are 00 and 11. This language does not accept null, 0, or 1.

Single 0's or 1's means words with either 0's or 1's without null. Double 0's or 1's means clumps of letters that will always come together.

It depends on the expression given to us.

There is not any formal procedure to know the number of states. This ability improves with time and practice.

Transition means which letter, after being read, is transferred from which place to which place. It is necessary to show the transition of every letter from each state.

No, if any state starts from the final state, it does not accept any string. It does not accept the null string either, as there is no path starting from the initial state and ending in the final state.

A Finite Automaton (FA) should accept all words of the language and reject all words not part of the language. Any FA meeting these criteria is suitable for the language.

The DEAD STATE is introduced to be able to make an automaton complete without altering its behavior.