### LEXICAL ANALYSIS

**Tokens.** The lexical analyzer scans the source program and produces as output a sequence of tokens, which are normally passed, one at a time to the parser. Some tokens may consist only of a token name while others may also have an associated lexical value that gives information about the particular instance of the token that has been found on the input.

**Lexemes. **Each time the lexical analyzer returns a token to the parser, it has an associated lexeme – the sequence of input characters that the token represents.

**Buffering. **Because it is often necessary to scan ahead on the input in order to see where the next lexeme ends, it is usually necessary for the lexical analyzer to buffer its input. Using a pair of buffers cyclicly and ending each buffer’s contents with a sentinel that warns of its end are two techniques that accelerate the process of scanning the input.

**Patterns. **Each token has a pattern that describes which sequences of characters can form the lexemes corresponding to that token. The set of words, or strings of characters, that match a given pattern is called a language.

**Regular Expressions. **These expressions are commonly used to describe patterns. Regular expressions are built from single characters, using union, concatenation, and the Kleene closure, or any-number-of, operator.

**Regular Definitions. **Complex collections of languages, such as the patterns that describe the tokens of a programming language, are often defined by a regular definition, which is a sequence of statements that each define one variable to stand for some regular expression. The regular expression for one variable can use previously defined variables in its regular expression.

**Extended Regular-Expression Notation.** A number of additional operators may appear as shorthands in regular expressions, to make it easier to express patterns. Examples include the + operator (one-or-more-of), ? (zero-or-one-of), and character classes (the union of the strings each consisting of one of the characters).

**Transition Diagrams. **The behavior of a lexical analyzer can often be described by a transition diagram. These diagrams have states, each of which represents something about the history of the characters seen during the current search for a lexeme that matches one of the possible patterns. There are arrows, or transitions, from one state to another, each of which indicates the possible next input character that cause the lexical analyzer to make that change of state.

**Finite Automata. **These are a formalization of transition diagrams that include a designation of a start state and one or more accepting state, as well as the set of states, input characters, and transitions among states. Accepting state indicate that the lexeme for some token has been found. Unlike transition diagrams, finite automata can make transitions on empty input as well as on input characters.

**Deterministic Finite Automata.** A DFA is a special kind of finite automaton that has exactly one transition out of each state for each input symbol. Also, transitions on empty input are disallowed. The DFA is easily simulated and makes a good implementation of a lexical analyzer, similar to a transition diagram.

**Nondeterministic Finite Automata**. Automata that are not DFA’s are called nondeterministic. NFA’s often are easier to design than are DFA’s. Another possible architecture for a lexical analyzer is to tabulate all the states that NFA’s for each of the possible patterns can be in, as we scan the input characters.

**Conversion Among Pattern Representations.** It is possible to convert any regular expression into an NFA of about the same size, recognizing the same language as the regular expression defines. Further, any NFA can be converted to a DFA for the same pattern, although in the worst case (never encountered in common programming languages the size of the automaton can grow exponentially. It is also possible to convert any nondeterministic or deterministic finite automaton into regular expression that defines the same language recognized by the finite automaton.

**Lex. **There is a family of software systems, including Lex and Flex, that are lexical-analyzer generators. The user specifies the patterns for tokens using an extended regular-expression notation. Lex converts these expressions into a lexical analyzer that is essentially a deterministic finite automaton that recognizes any of the patterns.

**Minimization of Finite Automata.** For every DFA there is a minimum-state DFA accepting the same language. Moreover, the minimum-state DFA for a given language is unique except for the names given to the various states.