DFA Minimization
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The document discusses determining equivalent states in a deterministic finite automaton (DFA) and using them to minimize the DFA. It provides an example of a DFA over the alphabet {a,b} recognizing strings with an even number of a's. The states {[Ea,Eb], [Ea,Ob]} and {[Oa,Eb], [Oa,Ob]} in this DFA are equivalent and can be collapsed into single states, creating a smaller minimal DFA with equivalent state partitions. The example DFA is then refined step-by-step to show the equivalent state partitions.
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![Strings over { a,b } with even number of a ’s * Ea Oa Eb Ob Ob Eb b b b b a a a a [Oa,Ob] [Ea,Eb] [Ea,Ob] [Oa,Eb]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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The document discusses three programming language translators: assemblers translate assembly language into machine code, compilers translate high-level languages into executable object code, and interpreters execute instructions one at a time without producing an executable file. Assemblers convert mnemonics to machine language equivalents and assign addresses, compilers check syntax and generate all code at once, and interpreters check keywords and convert instructions individually to machine code.
Intermediate code generation
The document discusses intermediate code in compilers. It defines intermediate code as the interface between a compiler's front end and back end. Using an intermediate representation facilitates retargeting a compiler to different machines and applying machine-independent optimizations. The document then describes different types of intermediate code like triples, quadruples and SSA form. It provides details on three-address code including quadruples, triples and indirect triples. It also discusses addressing of array elements and provides an example of translating a C program to intermediate code.
Translators(Compiler, Assembler) and interpreter
This document provides information on different types of translators - assemblers, compilers, and interpreters. It discusses:
- Assemblers translate assembly language to machine code and check for errors. The output is called object code.
- Compilers translate high-level languages to machine code in a lengthy process, generating errors if needed. Object code is produced.
- Interpreters translate each instruction as the program runs, without producing object code. Errors can be found more easily than with compilers.
Lexical analyzer
The document discusses the different phases of a compiler including lexical analysis, syntax analysis, semantic analysis, intermediate code generation, code optimization, and code generation. It provides details on each phase and the techniques involved. The overall structure of a compiler is given as taking a source program through various representations until target machine code is generated. Key terms related to compilers like tokens, lexemes, and parsing techniques are also introduced.
Lexical analyzer
The document discusses the role and process of lexical analysis in compilers. It can be summarized as:
1) Lexical analysis is the first phase of a compiler that reads source code characters and groups them into tokens. It produces a stream of tokens that are passed to the parser.
2) The lexical analyzer matches character sequences against patterns defined by regular expressions to identify lexemes and produce corresponding tokens.
3) Common tokens include keywords, identifiers, constants, and punctuation. The lexical analyzer may interact with the symbol table to handle identifiers.
Code generation
The document discusses code generation in compilers. It describes the main tasks of the code generator as instruction selection, register allocation and assignment, and instruction ordering. It then discusses various issues in designing a code generator such as the input and output formats, memory management, different instruction selection and register allocation approaches, and choice of evaluation order. The target machine used is a hypothetical machine with general purpose registers, different addressing modes, and fixed instruction costs. Examples of instruction selection and utilization of addressing modes are provided.
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DFA Minimization
- 2. Strings over { a,b } with even number of a ’s * Ea Oa Eb Ob Ob Eb b b b b a a a a [Oa,Ob] [Ea,Eb] [Ea,Ob] [Oa,Eb]
- 3. Strings over { a,b } with even number of a ’s * Ea Oa a a [Ea] [Oa] b b
- 6. Main Idea qi qn qj qm If qm and qn are distinguishable, then so are qi and qj a a
- 7. Example DFA q0 q4 q1 q2 q3 q7 q5 q6 a b a a,b a a,b b b b a b (a u b)(a u b * ) a,b a
- 9. Example DFA showing equivalent states q0 q4 q1 q2 q3 q7 q5 q6 a b a a,b a a,b b b b a b (a u b)(a u b * ) a,b a
- 10. Example Minimum DFA q0 q1,q4 q7 q2,q5 q3,q6 a a,b a a,b b a,b b (a u b)(a u b * )