[PDF] 10 Reducibility HALTTM is not Turing-decidable.

Homework 10 Solutions

Observe that A is a context-free language so it is also Turing-decidable. Thus

CS 341: Foundations of CS II Marvin K. Nakayama Computer

Typical approach to show L is undecidable via reduction from ATM to L. Suppose L is decidable. Universe ? = {?M?

COMPSCI 501: Formal Language Theory Reducibility so far

4 mars 2019 Reducibility: a tool to show undecidability ... reduce ATM to HALTTM ... Turing machine M on input w

Mapping Reducibility ETM = {

by creating a decider S of ATM: some Turing machine M on every input w

5.4 No. For example consider A = {0 1

5.5 Show that ATM is not mapping reducible to ETM. I will be using the ¬ symbol ATM is Turing recognizable but not co-Turing recognizable. The TM below.

ECS120 Discussion Notes

28 nov. 2006 Lets do this reduction more formally now and give a computable function that shows ATM ?m ETM. First

Computability Theory

assumption to show that ATM is decidable contradicting Theorem Example 6.19 shows that ETM is Turing reducible to ATM. Computability Theory.

10 Reducibility

HALTTM is not Turing-decidable. Proof: We will reduce ATM to HALTTM. Assume TM R decides HALTTM. We construct TM S that decides ATM as follows: On 

1 Mapping reducibility Definition 1 A function f : ? ? ? ?? is a com

Since f is a mapping reduction ATM ? EQTM it is also a mapping reduction ATM ? EQTM. Hence

CS 301 - Lecture 22 – Mapping reductions

What we've called a reduction up until now is also called a Turing reduction. Theorem Show that ETM ?m EQTM by giving a TM T that computes the mapping.

reductions3-print - Stanford University

One can often show that a language Lis undecidableby showing that if L is decidable then so is ATM We reduceATM to the language L ATM ? L We showed:ATM ? HALT TM Mapping Reductions ??* is a computable functionif there is a Turing machine M that halts with just f(w) written on its tape for every input w A language A is mapping reducible to

Homework 8Solutions

show that some other problem already known to be undecidable reduces to UNDECIDABLE PROBLEMS FROM LANGUAGE THEORY We have already established the undecidability of ATM the problem of mining whether a Turing machine accepts a given input Let's consider a problem HALT TM the problem of determining whether a Turing machine

Homework 10 Solutions - New Jersey Institute of Technology

2 Show that A TM is not mapping reducible to E TM In other words show that no computable function reduces A TM to E TM (Hint: Use a proof by contradiction and facts you already know about A TM and E TM ) Answer: Suppose for a contradiction that A TM m E TM via reduction f This means that w 2A TM if and only if f(w) 2E TM which is

Lecture Notes: The Halting Problem; Reductions

Intuitively for recognizability we allow our TM to run forever on inputs that are not inthe language while for decidability we require that the TM halt on every input Now recall our two most important results: Theorem 1 There exist (uncountably many!) languages which are not Turing-recognizable

Undecidable Languages - University of Washington

Show ATMis reducible to AH(Theorem 5 1 in text) Suppose Ais decidable Hthere’s a decider MHfor A H Then we can construct a decider DTMfor ATM: On input run M on If MHrejects then REJ (this takes care of M looping on w) If MHaccepts then simulate M on w until M halts If M accepts then ACC input ; else REJ

Searches related to show that etm turing reduces to atm filetype:pdf

We show A TM reduces to E TM Proof: Assume E TM is decidable with TM R We show then that A TM is decidable a contradiction • Using R we construct a TM M ATM that decides A TM: M ATM = Correctness: M ATM is a decider since R is and accepts iff L(X) is nonempty iff M accepts w • But A TM is undecidable a

Is there a Turing machine that recognizes ETM?

Answer: We need to show there is a Turing machine that recognizes ETM, the com- plement of ETM. Let s1,s2,s3,... be a list of all strings in ??. For a given Turing machine M, we want to determine if any of the strings s1,s2,s3,... is accepted by M.

What is a mapping reduction in Turing machine?

Turing machine M that halts with just f(w) written on its tape, for every input w. language A is mapping reducibleto language B, written A ?mB, if there is a computable f : ?* ??*, such that for every w, ?A ?f(w) ?B is called a mapping reduction (or many8one reduction) from A to BLet f : ?* ??* be a computable functionsuch that w ?A ?f(w) ?B

How to improve the security of the ATM system?

The original password authentication method combined with the biometric technology for identification in the ATM machine has improved the security of the transaction with increasing emphasizes given to security automated personal identification needs to be added to the traditional ATM system to overcome its disadvantages.

What is ATM tampering?

The term refers to low-level operators within a criminal organization who are assigned high-risk jobs, such as installing ATM skimmers and otherwise physically tampering with cash machines.