1. The L1 language defined as follows: L2={wcwRw(0+1)} Find the grammar and the PDA (pushdown automata) that derives this language. 2. Construct the transition diagram of NFA recognizing the following regular expressions. a) P1=a(bcb+cbc) b) P2=0+1(01)1 3. Let the finite state machine M be defined as the machine that recognizes strings ending with 11,101 , or 110 in the alphabet {0,1}. a) Construct the non-deterministic (NFA) transition diagram of M using as few states as possible. b) Write the regular language recognized by the M machine as a regular expression. 4. Let the L2 language be defined by the following regular expression: L2=a(bb+cc)d a) Construct the transition diagram of the finite automata (NFA) that recognizes the L2 language. (in the diagram, name the initial state as S and the other states as A,B,C, ) b) If the diagram you created contains - transitions, find the equivalent transition diagram without - transition by eliminating the - transitions in the transition diagram