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55+Notes+on+PS7+_6 - Incorrect Solutions for Problem Set 7...

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Incorrect Solutions for Problem Set 7 Problem 6 1. Follow a method similar to the one used for DFAs: a) mark the start state b) mark all states that have incoming transitions from marked states c) repeat step (b) until no new states are marked d) accept if there exist any unmarked states; otherwise, reject Why this fails A state in a PDA may be unused despite having a transition leading to it from a reachable state. Consider this simple PDA: In this example, there is a transition from g1869 g2869 leading to g1869 g2870 ; however, this transition is only followed when the character g1854 is on the stack. Since there is no mechanism in this PDA for placing g1854 on the stack, g1869 g2870 is never actually used. The solution outlined above would incorrectly conclude that this example has no unused states. 2. Convert the PDA to a CFG and use an algorithm to determine whether the given CFG includes any unused variables (or transitions, or terminals, etc…), accepting if it does and rejecting otherwise.

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