Turing Machines- Cont. Theory of Computation Lecture 11 Tasneem Ghnaimat

Definitions Usually we assume that after going to a final state, the TM halts, i.e., it makes no more moves. A string w will not be accepted by the TM, if it reaches a state from which it cannot make a next move. Or while reading w, the TM gets into a loop and is never able to halt. Tasneem Ghnaimat

Decidability A language is decidable, if there is a Turing machine (decider) that accepts the language and halts on every input string Tasneem Ghnaimat Turing Machine Input string Accept Reject YES NO Decider for

Tasneem Ghnaimat Undecidable Languages there is no Turing Machine which accepts the language and makes a decision (halts) for every input string undecidable language = not decidable language There is no decider:

Examples of Decidable Problems Decidable: {1,3,5}  {x | x is even} {x | x is a perfect square} {x | x 2 -10x = 0} {x | x=y * z for some integers y,z>1 (i.e. x is not prime)} {x | x is a prime (i.e. x is not divisible by anything except 1 and itself)} { | G is a connected graph} { | P is a one-variable polynomial expression with an integral root} Undecidable: { | P is a two-variable polynomial expression with an integral root}