How should we define the behavior of a Turing machine where the head tries to move left from the leftmost tape position?

If we have a Turing machine in a model with a tape that is infinite only to the right and assume at some point the head tries to move left from the leftmost position.

How should we define the behavior in such a case? Is a machine doing so for some input not a valid Turing machine? And if so, how can we make sure when we define a Turing machine that this situation can’t occur for any input?

I’ve read some sources about Turing machines though couldn’t find the answer to this specific case, and I see no reason why this case won’t happen for an arbitrary Turing machine and some input.

A Wayback Machine Backup Of My Old GSA SER Tutorials.

I need my personal blog for my new project and YouTube channel and I’m going to start it over from scratch next month so here is a Wayback machine backup for all of my old GSA SER Tutorials if anyone needs them.

The Importance Of Using Naming Conventions In SER! – https://web.archive.org/web/20200520204634/http://shaunmarrs.com/naming-conventions-ser/
My Opinion On Reverse Proxies And How To Use Them In GSA Search Engine Ranker! – https://web.archive.org/save/http://shaunmarrs.com/opinion-reverse-proxies-using-gsa-search-engine-ranker/
How To Build The Ultimate Auto Accept List For SEO Tools! – https://web.archive.org/web/20200520205025/http://shaunmarrs.com/ultimate-auto-accept-list/
How To Build Your Own Auto Accept List With GSA Search Engine Ranker! – https://web.archive.org/web/20200520205113/http://shaunmarrs.com/auto-accept-list-ser/
How I Choose, Setup And Optimise My VPS’ And Servers! – https://web.archive.org/web/20200520205209/http://shaunmarrs.com/setup-and-optimise-vps/
An Introduction To Building Your Own Auto Accept List! – https://web.archive.org/web/*/http://shaunmarrs.com/introduction-building-own-list/
Transforming Profile and Forum Engines In To Contextuals In Less Than 30 Seconds! – https://web.archive.org/web/2019*/http://shaunmarrs.com/profile-and-forum-contextual/
The True Indexing Potential Of The GSA SER Platforms! – https://web.archive.org/web/2019*/http://shaunmarrs.com/indexing-ser-platforms/
The Difference Between Getting 1% Or 98% Of Your Links Indexed! – https://web.archive.org/web/2019*/http://shaunmarrs.com/1-and-98-of-your-links-indexed/
The Kitchen Sink Tier And How 97% Of Their Links Maybe Useless To You! – https://web.archive.org/web/2019*/http://shaunmarrs.com/why-i-hate-kitchen-sink/
The Increasing Problem Of Link Retention When Using Auto Generated Content! – https://web.archive.org/web/2019*/http://shaunmarrs.com/link-retention-auto-generated-content/
How To Filter Out Useless Footprints To Massively Improve Your Target Scraping Speed! – https://web.archive.org/web/2019*/http://shaunmarrs.com/footprints-in-gsa-search-engine-ranker/
How To Easily Post To Self Hosted Domains With GSA Search Engine Ranker – https://web.archive.org/web/2019*/http://shaunmarrs.com/post-to-self-hosted-domains/
607 Links Per Minute With Free Public Proxies! – https://web.archive.org/web/2019*/http://shaunmarrs.com/case-study-public-proxies/
How To Easily Manage All Your Backlinks In One Place! – https://web.archive.org/web/2019*/http://shaunmarrs.com/how-to-easily-manage-all-your-backlinks-in-one-place/
A 5 Second Task To Strengthen Your Contextual Tiers In GSA Search Engine Ranker. – https://web.archive.org/web/2019*/http://shaunmarrs.com/contextual-engine-selection-in-gsa-search-engine-ranker/
How To Build Tier Three Projects That Run At Over 900 Links Per Minute! – https://web.archive.org/web/2019*/http://shaunmarrs.com/944-links-per-minute/
Stop Wasting Your Time With The Built In GSA Search Engine Ranker No Follow Filter – https://web.archive.org/web/2019*/http://shaunmarrs.com/gsa-search-engine-ranker-no-follow-filter/
How To Increase The Quality Of The Targets On Your GSA Search Engine Ranker List! – https://web.archive.org/web/2019*/http://shaunmarrs.com/increasing-the-domain-quality/
An Increase Of 223% In Contextual Verified Links Per Minute With GSA Search Engine Ranker! – https://web.archive.org/web/2019*/http://shaunmarrs.com/increase-in-contextual-verifieds-per-minute/
Why The Native GSA Search Engine Ranker Web 2.0 Engines Are A Waste Of Time! – https://web.archive.org/web/2019*/http://shaunmarrs.com/gsa-search-engine-ranker-web-2-0-engines/
GSA Search Engine Ranker, The Ultimate Metrics Per Minute Breakdown! – https://web.archive.org/web/2019*/http://shaunmarrs.com/metrics-per-minute-showdown/
Essential GSA Search Engine Ranker Maintenance To Keep Your Rig Running Smoothly! – https://web.archive.org/web/2019*/http://shaunmarrs.com/gsa-search-engine-ranker-maintenance/
From 76 LPM to 763 LPM With GSA Search Engine Ranker Using A Simple 12 Hours Process! – https://web.archive.org/web/2019*/http://shaunmarrs.com/from-75-77-lpm-to-763-33-lpm-in-gsa-search-engine-ranker/
How To Filter Your GSA Search Engine Ranker Lists For A Potential 963% Increase In LPM! – https://web.archive.org/web/2019*/http://shaunmarrs.com/how-to-filter-your-gsa-search-engine-ranker-lists/
A Little Role Play To Explain Why You Should Filter Your GSA SER Verified Lists. – https://web.archive.org/web/2019*/http://shaunmarrs.com/a-little-role-play-to-explain-why-you-should-filter-your-gsa-ser-verified-lists/
The Ultimate Guide To GSA Search Engine Ranker! – https://web.archive.org/web/2019*/http://shaunmarrs.com/the-ultimate-guide-to-gsa-search-engine-ranker/

Maximum characters in a deterministic Turing machine

Assume we have a deterministic Turing machine $ M = (q_s, q_a, q_r, \Sigma, \Gamma, \delta, Q, b)$ where $ q_s,q_a,q_r$ are the (unique) starting state, accept state and reject state respectively, $ Q$ the set of non-final states, $ \Sigma$ the input alphabet, $ \Gamma$ the tape alphabet, $ \delta$ the transition function and $ b \in \Gamma$ the blank symbol.

How many characters can fit in $ \Gamma$ , as a function of $ |\Sigma|, |Q|$ such that for each $ c \in \Gamma$ , $ \delta$ will be defined by it for some state and character?

How to proof that Turing machine that can move right only a limit number of steps is not equal to normal Turing machine

I need to prove that a Turing machine that can move only k steps on the tape after the last latter of the input word is not equal to a normal Turning machine.

My idea is that given a finite input with a finite alphabet the limited machine can write only a finite number of “outputs” on the tape while a normal Turing machine has infinite tape so it can write infinite “outputs” but I have no idea how to make it a formal proof.

any help will be appreciated.

Question on the decidable of Turing Machine

I am a bit confused about using the subset of the turning machine to prove the desirability of the turning machine.

If I have a Turing Machine M and we have already know M has a single halting state. If we already the machine takes a string was the input and reaches to the state q0, is it possible to prove that M is decidable by considering constructing a new Turing Machine that halts on q0?

Thanks a lot!

Is solving a quadratic equation using Turing machine impossible?

I’ve just started Algorithms at university. There’s a task to write an algorithm for a Turing machine to solve quadratic equations. The task doesn’t specify if it’s x^2+bx+c or ax^2+bx+c. I’ve searched whole bunch of information over Russian and English Internet.

I did find articles, which say it’s not possible because we’ve got real numbers A, B, C. Please confirm if that’s true. I may not get it correct.. But I think that’s impossible. I still don’t know how to prove my thoughts.

Thanks in advance!

If anything can be verified efficiently, must it be solvable efficiently on a Non-Deterministic machine?

Suppose, I wanted to verify the solution to $ 2$ ^$ 3$ . Which is $ 8$ .

The $ powers~of~2$ have only one 1-bit at the start of the binary-string.

Verify Solution Efficently

n = 8 N = 3 IF only ONE 1-bit at start of binary-string:   IF total_0-bits == N:    if n is a power_of_2:      OUTPUT solution verified, 2^3 == 8 

A solution will always be approximately $ 2$ ^$ N$ digits. Its not possible for even a non-deterministic machine to arrive to a solution with $ 2$ ^$ N$ digits faster than $ 2$ ^$ N$ time.

Question

Can this problem be solved efficently in non-deterministic poly-time? Why not if the solutions can be verified efficently?

NTM Machine for 3D

How can we design NTM for color theorem that checks for 3 dimension map(Assume we have 3 dimension map where there are cities in the sky as well). How can we check if the map can be colored by 10 colors?