L = {<M> | exists x s.t M traverse all states on M(x)}
http://tau-cm2012.wikidot.com/forum/t-521574/l-m-exists-x-s-t-m-traverse-all-states-on-m-x
Posts in the discussion thread "L = {<M> | exists x s.t M traverse all states on M(x)}"Tue, 29 Sep 2020 14:31:09 +0000http://tau-cm2012.wikidot.com/forum/t-521574#post-1507051(no title)
http://tau-cm2012.wikidot.com/forum/t-521574/l-m-exists-x-s-t-m-traverse-all-states-on-m-x#post-1507051
Fri, 13 Jul 2012 12:22:05 +0000idan
L in RE because it has a verifier. (OR - run lexi. all words, hold a counter for each word, if a word's counter reaches Q - accept). NOT in R:(suggestion) comp.Atm < comp.L = {<M>. for all x, exists a state q never reached} (if true - compl.L not in R==> L not in R) for input <M,w> output Mw - a Universal machine that will run M +Qt (- a state that uses epsilon transitions to traverse all states in Mw) for input x, Mw emulates M(w) x steps. if M accepts (<M,w> not in comp.Atm)==>goto Qt and traverse all states (Mw not in comp.L) correctness: <M,w> in compl.Atm==> no such x causing reaching Qt (Qt is the state never traversed)==> <Mw> in comp.L <M,w> not in comp.Atm==>exists x that traverses all states in Mw==><Mw> not in comp.L

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http://tau-cm2012.wikidot.com/forum/t-521574#post-1507008(no title)
http://tau-cm2012.wikidot.com/forum/t-521574/l-m-exists-x-s-t-m-traverse-all-states-on-m-x#post-1507008
Fri, 13 Jul 2012 10:27:08 +0000Ella
Not decidable because if you consider the complement language: "…for all x M never traverse all states…" How can you check it? What if M doesnt halt on x? Im not sure, but my guess here is that its in RE, given M halts on x, I can check if M had traversed all states….
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http://tau-cm2012.wikidot.com/forum/t-521574#post-1506980L = {<M> | exists x s.t M traverse all states on M(x)}
http://tau-cm2012.wikidot.com/forum/t-521574/l-m-exists-x-s-t-m-traverse-all-states-on-m-x#post-1506980
Fri, 13 Jul 2012 08:30:42 +0000Netanel
Can someone please explain why this language is Undecidable? And to which class it belongs? RE, CoRE, not in RE nor in CoRE?
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