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1. Simulate a TM with infinite tape on both ends using a two-track TM with finite storage
2. Prove the following language is non-Turing recognizable using the diagnolization principle { (M, w) | TM M, starts with input w, does not halt}
3. Construct a TM for L = {w| w contains equal number of 0's and 1's} over {0,1} a) provide an algorithmic description b) draw the transition diagram
4. Consider a language L = {0m10n10max(m,n)| m, n>= 0}. Construct a TM that decides the language. Describe the algorithm and draw the transition diagram of the TM.
5. Given the following TM M, does M a) accept or b) reject on inputs w1 = 000 and w2=0000? Show the content of the input tape and positions of the head step-by-step.
Sketch an algorithm for the universal recognition problem for SL 2 . This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwi
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De?nition Deterministic Finite State Automaton: For any state set Q and alphabet Σ, both ?nite, a ?nite state automaton (FSA) over Q and Σ is a ?ve-tuple (Q,Σ, T, q 0 , F), w
We now add an additional degree of non-determinism and allow transitions that can be taken independent of the input-ε-transitions. Here whenever the automaton is in state 1
To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the
Given any NFA A, we will construct a regular expression denoting L(A) by means of an expression graph, a generalization of NFA transition graphs in which the edges are labeled with
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