I want to know if there can be 2 or more GMT timezones for one city or state. I know there can be more then one GMT timezone for a country, but not sure if it's for state and city too. Share your knowledge please.
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Have a look at http://www.worldtimezone.com/faq.html
Any arbitrary jurisdiction may have multiple timezones, though the majority do not.
Interpreting the question to mean 'are there any cities which are in more than one time zone', then the answer is 'yes'. And there are American states with multiple time zones (Indiana and Arizona being two of them).
There has been recent discussion on the TZ mailing list about the area of China known as Xinjiang, which has a mixed population of Han Chinese and of Uyghurs. It seems that the Han use the standard Chinese time zone (Asia/Beijing), but the Uyghurs often use a local time zone. This is now encapsulated in the Olson database, with the name Asia/Urumqi for the Uyghur time zone.
So, for example, the zone.tab file in tzdata2010b.tar.gz, available from ftp://elsie.nci.nih.gov/pub/tzdata2010b.tar.gz (the code is ftp://elsie.nci.nih.gov/pub/tzcode2009t.tar.gz). There is an extensive description of how and why the change was made in the asia file.
Note that the Olson (Time Zone) database is now (2016-09-19) available from IANA at https://www.iana.org/time-zones rather than from NIH. You can get the current release easily enough; getting historical releases may be harder.
Yes, time zones really do change 20 times a year around the world, and sometimes at essentially no notice (that is, the government legislates the changes only a day or two before the change).
@basit asks:
What I mean is that during the course of 2009, there were 20 issues of the time zone database, because of changes in rules in at least that many places. However, any given country usually only changes their rules once - though with Argentina, different states were changing their rules at different times and compounding the problems.
I'm not clear that we have enough information to tell you how long to log the data for. I'd be inclined to say at least 12 months, but it depends what you are going to do with it. At one level, all you need to do is keep up with the Olson database - that will tell you the time zone rules for essentially everywhere in the world. If you are interested in tracking the time zones of your visitors, then you can keep the data for as long as you like. Since not everyone uses the canonical Continent/City notation for their time zone (I tend to use the older US/Pacific notation, for instance - which is still supported, but is equivalent to America/Los_Angeles). The classical notations such as TZ=EST5EDT are ambiguous; both the USA and Australia have timezones that use EST as an abbreviation, and the dates when the switch between standard and daylight saving time occurs varies (witness the mass of data in the Olson database).
You also ask 'how long does it take for a time zone to change'. I'm not sure what you mean. In terms of 'when the clocks change (between standard and daylight saving time)', it is 'instantaneous'; one second it is one time zone offset; the next second it is the other. If you mean 'how long does it take for governments to change their mind', it varies radically. For example, both Europe and the USA have relatively fixed rules that change every few years; the rule in the USA had been stable for about 20 years, then they changed the rules about 3 years ago. Europe is similar. On the other hand, some countries change their rules yearly. My impression is that some of the Islamic countries adjust when they switch between standard and daylight saving time (or vice versa) depending in part on when Ramadan falls - if the change would occur during Ramadan, then they bring it forward, or delay it, so that the rule does not change during Ramadan. Other countries have different reasons for the brinksmanship that goes on - maybe it is the political equivalent of a release deadline. So it may take quite a while for people to decide what the 'final' (meaning 'next edition') of the rules will be for a given year.
The web site http://worldtimezone.com/ does a pretty good job of keeping track of most of these idiosyncracies.
I think you mean "Can one city or state span two time zones?". Yes. Mexico Beach, FL sits on the border between CST and EST with parts of the town in both time zones.
As for how you could tell a computer that, no idea.
There is only one gmt for the whole world. As for timezones, see here, showing variation of observance e.g. within Kansas.