CMPS 260 Spring 2022
Programming Assignment: DFA Simulation
Deadline: 11:59pm, Friday, April 22

Provided are the following Java classes, the first three of which you are to complete. (Each one has one or more method stubs.)

• DFA_Semi: An instance of this class represents a semi-DFA, which is, essentially, the transition function of a DFA. In other words, it is a DFA except that the initial state and final states have been left unspecified. States are identified by natural numbers starting at zero, as are the members of the input alphabet.
• DFA: A child class of DFA_Semi, an instance of this class represents a DFA. Thus, it augments its parent class with features pertaining to initial and final states.
• DFA_Utils: A class having methods that solve the decision problems that were the subjects of Problem 6 in HW #5.
• SetOverIntRange: An instance of this class represents a set of integers drawn from a universe that is a small range of integers. The DFA class has an instance variable of this type for the purpose of representing the set of final states. Also, its liveStates() method returns a value of this type.
• DFA_IO: A class that has static methods for reading a textual description of a DFA and consructing the corresponding instance of the DFA class, and, inversely, for writing a textual description of a DFA represented by an instance of the DFA class. Used by the DFA_Tester application.
• DFA_Tester: Java application whose purpose is to test the methods of the DFA class (including those inherited from its parent, DFA_Semi) and the DFA_Utils class.
• dfa1.txt, dfa2.txt, dfa3.txt, dfa4.txt: Files containing textual descriptions of DFAs, consistent with the format assumed by the DFA_IO class (and thus usable as input by DFA_Tester).

Notes

The methods in DFA_Utils are intended to solve the decision problems mentioned in Problem 6 of HW #5, for which sample solutions were provided. Don't ignore those sample solutions.

The liveStates() method in the DFA class is by far the most difficult part of this assignment. It is supposed to return the (IDs of the) set of "live" (i.e., non-dead) states in the DFA, which is to say those states from which a final state is reachable by some sequence of transitions.

Among the ways to solve the problem is to mimic the approach taken by the algorithms that identify nullable and fruitful nonterminals in a context-free grammar. A different —and superior in terms of running time— way to solve the problem is via a depth-first (or breadth-first) search.

Sample Execution of DFA_Tester:

The first line shows the program being invoked (in a command-line UNIX environment) and provided with the file name "dfa4.txt" as the command-line argument.

$ java DFA_Tester dfa4.txt This DFA has been loaded: ------------------------- Number of states: 5 Alphabet size: 2 delta(0,0) = 1 delta(0,1) = 0 delta(1,0) = 2 delta(1,1) = 3 delta(2,0) = 2 delta(2,1) = 4 delta(3,0) = 0 delta(3,1) = 3 delta(4,0) = 4 delta(4,1) = 4 Initial state: 0 Final states: {1} 0: Quit 1: Display DFA 2: Test deltaStar() in DFA_Semi 3: Test accepts() in DFA 4: Test hasMemberPrefix() in DFA_Utils 5: Test isSuffixOfMember() in DFA_Utils 6: Test isSubstringOfMember() in DFA_Utils 7: Test liveStates() in DFA >2 Enter state ID (-1 to quit, -2 to display DFA): 1 Enter input string: 110100 delta*(1,110100) = 2 Enter state ID (-1 to quit, -2 to display DFA): -1 0: Quit 1: Display DFA 2: Test deltaStar() in DFA_Semi 3: Test accepts() in DFA 4: Test hasMemberPrefix() in DFA_Utils 5: Test isSuffixOfMember() in DFA_Utils 6: Test isSubstringOfMember() in DFA_Utils 7: Test liveStates() in DFA >3 Enter input string (X to quit, Y to display DFA): 1101100 1101100 IS accepted. Enter input string (X to quit, Y to display DFA): 011010010 011010010 is NOT accepted. Enter input string (X to quit, Y to display DFA): X 0: Quit 1: Display DFA 2: Test deltaStar() in DFA_Semi 3: Test accepts() in DFA 4: Test hasMemberPrefix() in DFA_Utils 5: Test isSuffixOfMember() in DFA_Utils 6: Test isSubstringOfMember() in DFA_Utils 7: Test liveStates() in DFA >4 Enter input string (X to quit, Y to display DFA): 101 101 has a prefix that is a member. Enter input string (X to quit, Y to display DFA): 111 111 does not have a prefix that is a member. Enter input string (X to quit, Y to display DFA): X 0: Quit 1: Display DFA 2: Test deltaStar() in DFA_Semi 3: Test accepts() in DFA 4: Test hasMemberPrefix() in DFA_Utils 5: Test isSuffixOfMember() in DFA_Utils 6: Test isSubstringOfMember() in DFA_Utils 7: Test liveStates() in DFA >5 Enter input string (X to quit, Y to display DFA): 101 101 is not the suffix of any member. Enter input string (X to quit, Y to display DFA): 11110 11110 is the suffix of some member. Enter input string (X to quit, Y to display DFA): X 0: Quit 1: Display DFA 2: Test deltaStar() in DFA_Semi 3: Test accepts() in DFA 4: Test hasMemberPrefix() in DFA_Utils 5: Test isSuffixOfMember() in DFA_Utils 6: Test isSubstringOfMember() in DFA_Utils 7: Test liveStates() in DFA >6 Enter input string (X to quit, Y to display DFA): 110011 110011 is the substring of some member. Enter input string (X to quit, Y to display DFA): 000 000 is not the substring of any member. Enter input string (X to quit, Y to display DFA): X 0: Quit 1: Display DFA 2: Test deltaStar() in DFA_Semi 3: Test accepts() in DFA 4: Test hasMemberPrefix() in DFA_Utils 5: Test isSuffixOfMember() in DFA_Utils 6: Test isSubstringOfMember() in DFA_Utils 7: Test liveStates() in DFA >7 Live states are {0,1,3} 0: Quit 1: Display DFA 2: Test deltaStar() in DFA_Semi 3: Test accepts() in DFA 4: Test hasMemberPrefix() in DFA_Utils 5: Test isSuffixOfMember() in DFA_Utils 6: Test isSubstringOfMember() in DFA_Utils 7: Test liveStates() in DFA >0 Goodbye.