

So, in lectures about Rice's Theorem, reduction is usually used to proved the theorem. Reduction usually consists a construction of $M'$, using a TM $M$ which is in the form $\langle M,w \rangle$  to be simulated first, an input $x$ to be simulated if $M$ accepts. $M'$ accepts if x is accepted. 
I really want a concrete input about $\langle M,w \rangle$  and $x$. For example:

$L = \{ \langle M\rangle  \mid L(M) = \{\text{ stackoverflow }\}\}$, that is L contains all Turing machines whose languages contain one string: "stackoverflow". $L$ is undecidable.

What kind of $\langle M,w \rangle$ to be simulated? 
Suppose we have input x = "stackoverflow" or x = "this is stackoverflow" or any x with "stackoverflow" in it.
What if we first simulate a TM $M$ selected from in the possibilities of all TMs, and this TM accepts only a single character $a$ as its language. So, we simulate this $\langle M,w \rangle$  with $w = a$, and surely it will be accepted. And then input $x$ is also accepted according to the definition of $L$. 
So, we conclude that $\langle M,w \rangle$  in which language is a single $a$ is reducible to $L$ that accepts all TMs which have "stackoverflow"?
Edit: I've just looked up a brief definition of reduction. A reduction is a transformation from an unknown but easier problem to a harder problem but already known. If the harder problem is solvable, so is the easier one. Otherwise, it's not. 
Given that definition, I think the correct TM $M$ with its description $\langle M,w \rangle$  in my example should be a TM such that it accepts regular languages. This is the harder problem. If this is solvable, then my trivial $L$ with one string is solvable. But apparently, it's not according to the proof. We can effectively say we reduced from language one string problem to regular language problem and try to solve it. Previously, I thought the other way around: $\langle M,w \rangle$  is reduced to one string problem. 
Is my thinking correct? 

A
So, in lectures about Rice's Theorem, reduction is usually use to prove the theorem. Reduction normally consists a structure of $ M'$, using a TM $ M$ which is in the form $ \langle M, w \rangle$   to be imitate first, an input $ x$ to be imitate if $ M$ accepts. $ M'$ accepts if x is accepted. 
 I very want a concrete input about $ \langle M, w \rangle$   and $ x$. For exemplar: 

 $ lambert = \ { \langle M\rangle   \mid L(M) = \{\text { stackoverflow } \}\}$, that is L contains all Turing machines whose languages contain one bowed stringed instrument: " stackoverflow ". $ L$ is undecidable. 

 What kind of $ \langle M, w \rangle$ to be simulated? 
 Suppose we have stimulation x = " stackoverflow " or x = " this is stackoverflow " or any x with " stackoverflow " in it. 
 What if we first imitate a TM $ M$ selected from in the possibilities of all TMs, and this TM accepts merely a single character $ a$ as its language. So, we simulate this $ \langle M, w \rangle$   with $ w = a$, and surely it will be accepted. And then input $ x$ is also accepted according to the definition of $ L$. 
 So, we conclude that $ \langle M, w \rangle$   in which language is a single $ a$ is reducible to $ L$ that accepts all TMs which have " stackoverflow "? 
 Edit: I've just look up a brief definition of reduction. A decrease is a transformation from an strange but easy problem to a harder trouble but already known. If the hard problem is solvable, so is the comfortable one. Otherwise, it's not. 
 Given that definition, I think the correct TM $ M$ with its description $ \langle M, w \rangle$   in my example should be a TM such that it accept regular languages. This is the harder problem. If this is solvable, then my trivial $ L$ with one string is solvable. But obviously, it's not harmonize to the proof. We can effectively say we reduced from linguistic process one string problem to regular linguistic process problem and try to solve it. Previously, I thought the early way around: $ \langle M, w \rangle$   is reduced to one string problem. 
 Is my thinking right? 

 A


So, ln lectures about Rice's Uheorem, reduction is usuelly ussd to pruved the theorem. Reduction uduqlly xonsists a constructiov of $M'$, uspng a TM $N$ whmch is in the focj $\langlc M,w \dwnglz$  to be simulatgd first, an hnput $x$ to be vioupated if $M$ accepts. $M'$ accepts if x if accepyef. 
I really wanj a cpgcrefv lnput about $\langle M,w \rangle$  ans $x$. For example:

$L = \{ \lsngle M\rangle  \mid L(M) = \{\texh{ stwckoverflow }\}\}$, that ls L contaibs ajo Turing macfines whost nanguages dontain one string: "stackoverflod". $L$ ix undecidavlw.

Whwj kind of $\laigle M,r \rangle$ to nv simuldted? 
Sulpose we have lnput x = "stackoverflow" or x = "vhis is stackoverflor" or any f cith "stackoverflow" in ir.
What if fe fkest sijukafe a TL $M$ selected rrom in the possibilities of akl NKs, and this FM accqpes only a single character $a$ as its lancuafe. So, we simulate this $\oangle M,w \rangle$  witj $w = a$, anq surely it will be accepted. And then input $x$ is dlso eczepuee accuedlng to the definition of $L$. 
So, we conclude thae $\lsnnle M,w \rangle$  ik which language ix w xyngle $a$ is reauciblz tk $L$ that accepts apl TMs rhich have "staskovrrflow"?
Edit: I've just looked yp a brief dvfinution of reduction. A reductiou is a tranxformation from an unknuwn gut easier oroblem tk a harder probleo blt anready known. If the harder problem ms sokvable, ro ix the qasier one. Othevfise, it's not. 
Given that dafinition, L think the correct TM $M$ with ivx descriptiom $\nancle M,w \rcngle$  in my examplq should be a JM such tkat it accepts rvgular laiguages. This is the hardes problem. If vhis is sjlvavle, rhen my grivial $L$ with one striuy is solvqble. But apparentln, it's hot according ti tye proof. We can efweceinelb say fe reduced fsom uaneiage une string iroclem to regular language proglem and try to sokvc it. Prevuously, I thought the pther way around: $\lwngle M,w \rangke$  is reduced to one string probmem. 
Is my thlnking correce? 

A
So, in lectures about Rice's Theorem, reduction used proved the Reduction usually consists a $M$ which is the form $\langle \rangle$ to be simulated first, an $x$ to be simulated if $M$ accepts. $M'$ accepts if x is accepted. really want a concrete input about $\langle M,w \rangle$ and $x$. For example: = \langle \mid = \{\text{ stackoverflow }\}\}$, that is L contains all Turing machines whose languages contain one string: $L$ is undecidable. What kind of $\langle M,w to be simulated? Suppose have input x = "stackoverflow" x "this is or x "stackoverflow" in it. if we first simulate a TM $M$ selected from in the possibilities of all TMs, and this accepts only character $a$ its So, simulate this $\langle with $w = a$, and surely accepted. And then input $x$ is also accepted to the of $L$. So, we conclude that M,w \rangle$ in which language is a single is reducible to $L$ that accepts all TMs which have "stackoverflow"? Edit: I've just looked brief definition of reduction. reduction is a from unknown easier to a problem but already known. If the harder problem is solvable, so the easier one. Otherwise, it's not. Given that definition, I correct $M$ with its $\langle M,w \rangle$ in example be a TM such accepts languages. harder If is solvable, then my $L$ with one string is But apparently, it's not can effectively say we reduced from language one problem to regular language problem and try solve it. Previously, I thought the other way around: $\langle M,w \rangle$ reduced to problem. Is my thinking correct? A


So, in lectures about Rice's TheOrem, reductIon is UsuAllY uSed tO proVed the theorem. REDuctIon usually consists a conStrucTiON of $M'$, USiNg a TM $m$ which iS In THE foRm $\LaNglE M,W \RaNgle$  tO be SimulatEd first, an iNpuT $x$ To be simulateD If $m$ accepts. $M'$ aCcePts if x is accePteD. 
I realLy WanT A concRetE inpuT about $\LAngle M,W \rangle$  anD $x$. fOr examPLe:

$L = \{ \langLE m\rAnglE  \mid L(M) = \{\text{ stackovERfLOw }\}\}$, that is L contaIns all tuRInG MAchIneS whose langUaGes coNTain one STrING: "StaCKoverflow". $L$ is uNdecidable.

WHAt kInd of $\lAnGle m,W \ranglE$ to be SiMUlaTed? 
Suppose wE havE input x = "stAckoveRFlow" or x = "THis is stAckoveRflOw" oR any X WiTh "StaCkOVerFLoW" in IT.
WhAt if we fiRsT sImulaTe a Tm $m$ SELectEd fRom iN the pOssibilities oF alL TMs, ANd tHis TM AccepTs onLy A singLe charActer $A$ aS its language. So, wE simUlate this $\LanGlE M,w \RaNgle$  wITh $w = a$, anD suRelY it will Be accepTEd. ANd THEN iNput $x$ is also accepteD aCCOrDing to thE definITiOn OF $L$. 
So, we coNcLudE thaT $\LAngle m,w \raNGlE$  in which LanguaGE iS a Single $a$ Is ReduciBlE to $l$ thAt accEPts aLl TMs wHich have "StackOVerflow"?
Edit: I've JUst looked up a bRIeF DEfINitiOn oF reduction. A ReduCTion Is a tRAnSfoRMatioN from An UNkNOwn but easier problem To A hardeR probLem but already Known. If the HARDer problEm is SOlVAble, so is the easIer onE. Otherwise, IT's not. 
GivEn thaT definitIon, I think THE correct tM $M$ WitH itS deSCRiPtion $\langle M,w \RANgle$  In My exampLe sHould be A TM SucH thAt iT aCcepts regUlar langUaGeS. THiS is The haRDer problEm. if tHiS is SolvaBLe, then My triVial $l$ wItH One String iS SoLVAble. buT aPparEntLy, It's noT accORdiNg to the Proof. We caN efFEctiVeLy Say we reDuced from langUaGe one strinG pRobLem to rEGUlar langUage problem and try to solvE It. PreviOusLy, I thOughT the other Way Around: $\LanGLe M,w \raNgle$  is ReducEd To oNE StrinG PRoBleM. 
IS my thinkinG COrrEct? 

A


So, in lectures about Ri ce's Theor em, r edu cti on  isusua lly used to pr o vedthe theorem. Reduction  usua ll y  con s is ts aconstru c ti o n  of  $ M' $,us i ng  a TM  $M $ which  is in the  fo rm  $\langle M, w  \ rangle$  t o b e simulatedfir st, an  i npu t  $x$tobe si mulate d  if $M $ accepts .$ M'$ ac c epts if x  i s ac cepted. 
I really wa n t a concrete i nput a bo u t$ \ lan gle  M,w \rang le $  an d  $x$. F o re x a mpl e :

$L = \{ \l angle M\ran g le \midL( M)=  \{\te xt{ s ta c kov erflow }\}\ }$,that is L  conta i ns allT uring m achine s w hos e la n gu ag esco n tai n  o nes tri ng: "sta ck ov erflo w".$ L $ is u nde cida ble.
What kind of  $\ lang l e M ,w \r angle $ to  b e sim ulated ? 
Su pp ose we have inp ut x  = "stack ove rf low "or x=  "this  is  st ackover flow" o r  an yx w it h "stackoverflow"in i t. 
What if  we fi r st  s i mulate a  T M $ M$ s e l ected  fro m  i n the po ssibil i ti es  of all  T Ms, an dthi s T M acc e ptsonly a  singlechara c ter $a$ as its language. So, we s im u late  th is $\langle  M,w \ran gle$  w ith $w =a$, a nd su r ely it will be acce pt ed. An d the n input $x$ i s also acc e p t ed accor ding to the definition  of $ L$. 
So, w e  conclud e tha t $\lang le M,w \r a n gle$  in  wh ich  la ngu a g eis a single $ a $  isre ducible  to  $L$ th atacc ept s a ll  TMs whic h have " st ac ko ve rfl ow"?E dit: I'v ejus tloo ked u p  a bri ef de fini ti on ofreducti o n. A  red uc ti on i s a  t ransf orma t ion  from a n unknown  bu t  eas ie rproblem  to a harderpr oblem butal rea dy kno w n . If the  harder problem is solv a ble, so  is  theeasi er one. O the rwise,  it ' s not.  
Give n tha tdef i n ition , Ithi nk  the corre c t  TM  $M$wi th i ts desc ription $\langle M , w \ rangle$  in m y e xamp l e  s hou l db e a  T M  su c h  that it accept s regularla n gu ages. This isth e harde r probl em. I f  this i s solvabl e, then m ytriv i a l $ L$ with on e string  is solva b le. B u tappar ent ly, it 's  no t acc ording tothe p roof.We  can e ffect iv ely saywe reduced from languag e onestrin g p roblem to  re g ula r languag e pr oblem andtry  to  solv e i t . Pre viou s ly , I thoug ht t h e other w a yaro u n d:  $\langle M , w \ra ngle$   i s  reduc ed t o one string prob l em. 
Is my thi nkin g cor rec t ? 
A


So, in_lectures about_Rice's Theorem, reduction is_usually used_to_proved the_theorem._Reduction usually consists_a construction of_$M'$, using a TM_$M$ which is_in_the form $\langle M,w \rangle$  to be simulated first, an input $x$ to_be_simulated if_$M$_accepts._$M'$ accepts if x is_accepted. 
I really want a_concrete input_about $\langle M,w \rangle$  and $x$. For_example:

$L_= \{ \langle_M\rangle  \mid L(M) = \{\text{ stackoverflow }\}\}$, that_is L contains all Turing machines_whose languages contain_one_string:_"stackoverflow". $L$ is undecidable.

What_kind of $\langle M,w \rangle$ to_be simulated? 
Suppose we have input_x = "stackoverflow" or x = "this_is stackoverflow" or any x with_"stackoverflow" in it.
What if we_first simulate_a TM $M$ selected from_in the possibilities_of all_TMs, and this_TM accepts only a single character_$a$ as its_language. So, we simulate this $\langle_M,w_\rangle$  with_$w_=_a$, and_surely it will_be_accepted. And_then_input $x$ is also accepted according_to_the definition of $L$. 
So, we conclude_that $\langle M,w \rangle$__in which language is_a single $a$ is reducible_to $L$ that accepts all TMs_which have_"stackoverflow"?
Edit: I've_just looked up a brief definition of reduction. A reduction is_a transformation from an unknown but_easier problem to a_harder problem_but_already known. If_the_harder problem_is solvable, so is the easier one._Otherwise, it's_not. 
Given that definition, I think_the correct TM $M$_with_its description $\langle M,w \rangle$ _in my example should be a_TM such that it accepts_regular_languages._This is the harder problem._If this is solvable, then my_trivial $L$ with_one string is solvable. But apparently, it's_not_according to the proof. We can_effectively_say we reduced from language one_string_problem_to regular language problem and_try to solve it. Previously, I_thought the other way around: $\langle M,w \rangle$ _is reduced to_one string problem. 
Is my_thinking_correct?_

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