CMSC 330, Fall 2009
Organization of Programming Languages
Project 2 - Finite Automata Interpreter
You will need to implement a Finite Automata Interpreter that can build up NFAs, convert them to DFAs, minimize the DFAs, then test whether a string is accepted by the DFA.
Getting StartedDownload the following archive file p2.zip and extract its contents.
Along with files used to make direct submissions to the submit server (submit.jar, .submit, submit.rb), you will find the following project files:
Part 1: Extend the FiniteAutomaton class to support NFAsThe FiniteAutomaton class you downloaded is based on the DFA class used as an example during discussion section. The original DFA class was able to represent DFAs and run them to determine whether input strings are accepted by the DFA. You need to decide how to change/extend the FiniteAutomaton class to represent both NFAs and DFAs. Remember this means your class should support features in NFAs not in DFAs, such as epsilon-transitions and multiple transitions with the same label. You may choose to represent epsilon-transitions as transitions labeled with the empty string "" or some other label. You do not need to implement the ability to run NFAs on input strings, but you should be able to run DFAs on input strings I.e., the accept? method should return true if the string would be accepted and false otherwise if your FiniteAutomaton object is actually a DFA.
Part 2: Building NFAs out of other NFAsThe symbol! method for creating a new NFA for an individual symbol is provided. You need to add the ability to construct more complex NFAs from these single symbol NFAs. Three of the commands of the interpreter require the ability to create new NFA from existing NFA, using one of the following actions: concatenate, union, and closure. You need to implement the same functionality for NFAs represented by the FiniteAutomaton class in the methods concat! union! closure!. You must construct the new NFA using the algorithm discussed in lecture. For exmple, given two NFA a and b as follows:
You should be able to use the algorithm described in class to create a single NFA representing:
Note that though there are other algorithms for generating correct NFA for these operations, using them will yield a different NFA that will not pass the submit server tests. Your methods may (destructively) modify the current NFAs a and b. When you print out your NFA, you may notice differences between your output and the example output files provided in the public tests. The number assigned each state may be different, depending on the order you add new states to the FiniteAutomaton object. As a result, the order transitions are printed out may also differ. However, the submit server will ignore all output beginning with % (treating them as comments). So you can treat the FiniteAutomaton printout (which all begin with %) as diagnostic information that will not affect whether you pass a test.
Part 3: Reducing NFA to DFAOnce you have a NFA, invoking the toDFA method should create a new finite automaton representing a DFA created by the subset reduction method presented in class. I.e., the method should return a new FiniteAutomaton object that will accept only the strings accepted by the current FiniteAutomaton object, but which does not have epsilon-transitions or multiple transitions from a state with the same label.
Part 4: Minimizing DFAOnce you have a DFA, invoking the minimize! method should create a new finite automaton representing a minimal DFA created by the Moore reduction method presented in class. You may assume that the minimize! method will not be invoked on a NFA.
SubmissionYou can submit your project in two ways:
Hints and Tips
The Campus Senate has adopted a policy asking students to include the following statement on each assignment in every course: "I pledge on my honor that I have not given or received any unauthorized assistance on this assignment." Consequently your program is requested to contain this pledge in a comment near the top.
Please carefully read the academic honesty section of the course syllabus. Any evidence of impermissible cooperation on projects, use of disallowed materials or resources, or unauthorized use of computer accounts, will be submitted to the Student Honor Council, which could result in an XF for the course, or suspension or expulsion from the University. Be sure you understand what you are and what you are not permitted to do in regards to academic integrity when it comes to project assignments. These policies apply to all students, and the Student Honor Council does not consider lack of knowledge of the policies to be a defense for violating them. Full information is found in the course syllabus---please review it at this time.