Begin with a recursive definition of a path: EMPTY is a path and if p is a path and n is a local file identifier then the sequence obtained by appending  n to p (on the left) is a path.  And there are no other paths than the ones that can be built from a finite number of applications of this rule.  We can write “n/p” for the path obtained by appending n to p (appending on the left). Let’s require of course that the separator symbol “/” is not in any local file identifier. Other than that, there is no need to say anything at all about the set of file identifiers now – you can think of it as the set of strings that are “/” free if that helps, but they could be anything at all that is “/” free and can be connected into sequences. And  ”/” is just the name we use for the separator, it can be anything at all too.

UNIX style file systems are nearly always constructed on top of flat file systems. That is, we suppose we have a primitive set of “flat file names” of some sort and a map F that maps flat file names to the corresponding file contents.  Flat file names can be the same as local file identifier or different – it doesn’t matter. Right now we don’t have to say much about these flat file names at all but we have some demands on file contents. In particular, files need to be able to “encode”  lookup tables that relate local file identifiers to flat file names. Since we will require that a local file identifier appear at most once in such a table, we can think of the file contents as encoding a function- the “directory function”.  If “i” is a flat file name and F(i) is defined, we need to be able to associate F(i) with a type: plain or  directory (to start). Plain is just some data. If F(i) is defined, and F(i) has type directory, there is some function d= D(F(i))  we can decode from F(i) so that for some finite set of local file identifiers, “d” maps those identifiers to flat file names.

The idea is that we can start with some flat file name “i” and a path, say,  p=a/b/c and follow p from “i” as follows. First get i’=D(F(i))(a) if F(i) is a directory. Then get i”= D(F(i’))(b) and i”’= D(F(i”))(c) – assuming that the intermediate flat files are directories and they encode functions that map the flat file names “a”, “b” and “c”.  There’s some complexity because we’re not assured that everything will work out – we may only be able to follow a path partway before coming to a dead end.

So define a function R to take a flat file function F, an initial flat file name “i” and a path p and produces either a terminal flat file name or FAIL if the path cannot be followed all the way.  First we do the easy case R(F,i,EMPTY)= i.  The recursive case is

Associate F with a special flat file “r” – the root file. Then we can define U(p) = F(R(F,r,p)) if R(F,r,p) is not FAIL and let U(p)= FAIL otherwise.

And that’s it – except that now the flexible nature of the file system becomes clear. Let’s add a new file type “indirect” so that if F(i) is indirect, then we can extract a flat file map and a root flat file name from the contents. That is, if F(i) is an indirect file we can produce (F’,r’) = X(F(i)) where F’ is a flat file map and F’(r’) is a directory under F’.  Say “i” is a properly defined indirect file under F if and only if F(i) is indirect and for (F’,r)=X(F(i)) we have F’(r) as a directory. We can now redefine R as follows to switch flat file systems on an indirect file.

Note that the first definition of R is obviously primitive recursive – because we lose one element of the path sequence on each recursive step – but it’s not obvious that the version of R with indirect calls must terminate. The final condition on the indirect case assures us that at least every second step must remove one element from the path.

The A5 processor – the brain in the iPhone 4S and iPad 2 – is now made in a sprawling 1.6 million square feet factory in Austin owned by Korean electronics giant Samsung Electronics, according to people familiar with the operation.
One of the few major components to be sourced from within the United States, the A5 processor is built by Samsung in a newly constructed $3.6 billion non-memory chip production line that reached full production in early December

http://www.reuters.com/article/2011/12/16/us-apple-samsung-idUSTRE7BF0D420111216

 

A supply of tea with milk and sugar would be nice.  If it is tea I
really like, I like it without milk and sugar.  With milk and sugar,
any kind of tea is fine.  I always bring tea bags with me, so if we
use my tea bags, I will certainly like that tea without milk or sugar.

If I am quite sleepy, I would like two cans or small bottles of
non-diet Pepsi.  (I dislike the taste of coke, and of all diet soda;
also, there is an international boycott of the Coca Cola company for
killing union organizers in Colombia and Guatemala; see
killercoke.org.)  However, if I am not very sleepy, I won't want
Pepsi, because it is better if I don't drink so much sugar.

There’s more. A lot more.

http://en.wikipedia.org/wiki/Dennis_Ritchie

The US military’s unmanned Predator and Reaper drones are continuing to fly remote missions overseas despite a computer virus that has infected their US-based cockpits.
Government officials are still investigating whether the virus is benign, and how it managed to infect the heavily protected computer systems at Creech Air Force Base in Nevada, where US military pilots remotely fly the planes on their missions over Iraq, Afghanistan and elsewhere.
“Something is going on, but it has not had any impact on the missions overseas,” said a source, who was not authorized to speak publicly.
Armed tactical unmanned planes have become an increasingly valuable tool used by the US military to track and attack individuals and small groups overseas, but the virus underscores the vulnerability of such systems to attacks on the computer networks used to fly them from great distances.
Rob Densmore, former US navy airman, told Al Jazeera that the infection was a common keystroke logging virus – which registers the keystrokes pilots use to control the unmanned drones from afar.
“It has to have a point of access, so we know that thumb drives – basically USB drives – are used to upload navigational information, guidance information to Predator and Reaper drones.
“And if there’s a way somehow that that information, or that thumb drive, can come into contact with a network or with the internet, that’s where the danger is because that basically means that information can be carried across from the Reaper drones.”

http://english.aljazeera.net/news/americas/2011/10/201110816388104988.html

Government approach to security can be described as designing an unsinkable boat that has no doors between compartments and then, to make it usable, cutting a random and increasing number of undocumented holes between compartments.

A file is simply an ordered sequence of elements, where an element could be a machine word, a character, or a bit, depending upon the implementation. A user may create, modify or delete files only through the use of the file system. At the level of the file system, a file is formatless. All formatting is done by higher-level modules or by user-supplied programs, if desired. As far as a particular user is concerned, a file has one name, and that name is symbolic. (Symbolic names may be arbitrarily long, and may have syntax of their own. For example, they may consist of several parts, some of which are relevant to the nature of the file, e.g., ALPHA FAP DEBUG.) The user may reference an element in the file by specifying the symbolic file name and the linear index of the element within the file. By using higher-level modules, a user may also be able to reference suitably defined sequences of elements directly by context.

A directory is a special file which is maintained by the file system, and which contains a list of entries. To a user, an entry appears to be a file and is accessed in terms of its symbolic entry name, which is the user’s file name. An entry name need be unique only within the directory in which it occurs. In reality, each entry is a pointer of one of two kinds. The entry may point directly to a file (which may itself be a directory) which is stored in secondary storage, or else it may point to another entry in the same or another directory. An entry which points directly to a file is called a branch, while an entry which points to another directory entry is called a link. Except for a pathological case mentioned below, a link always eventually points to a branch (although possibly via a chain of links to the branch), and thence to a file. Thus the link and the branch both effectively point to the file. (In general, a user will usually not need to know whether a given entry is a branch or a link, but he easily may find out.)

?

Facebook engineers and analysts tap the company’s Hadoop clusters via a SQL-like query language known as Hive. [..]

Separate from its Hadoop work, Facebook built Cassandra, a distributed database also based on a piece of Google’s backend. Google uses a proprietary distributed database known as BigTable that runs atop the Google File System (GFS) system, and it published a paper on the technology in 2006. In echo of the Hadoop project, Facebook leaned on the paper in building Cassandra.

But Cassandra isn’t a pure BigTable mimic. Facebook applied BigTable’s data model to the Dynamo distributed storage system developed by Amazon for its S3 storage service, part of the retailer’s increasingly popular Web Services cloud. Cassandra’s authors included Avinash Lakshman, who helped build Dynamo at Amazon. Register

The Tile-Gx chips have 64-bit processing on their cores, and include floating point math instructions that allow a floating point operating to be done in five cycles instead of hundreds of cycles when done in software.

This is, believe it or not, important for PHP support, Ihab Bishara, director of cloud computing applications at Tilera, tells El Reg.

The Tile-Gx chips might support 64-bit processing, but physical memory addressing on the chips is either 39-bit or 40-bit, which works out to either 512GB or 1TB of maximum main memory. Each core burns less than a half watt of power. From the Register

All that work – to make PHP run faster and use less power.

We’ve heard three stories in which lead investors bailed on rounds after term sheets were signed.

 

The first upset came last week from a WeWork Labs company. The startup’s lead investor pulled out of a $500,000 round.

Another entrepreneur raised between $3 and $4 million and thought he was in the clear. The money was invested, but there was a draw-back clause on the term sheet.  The investor retracted all of the money 30 days later.

Today, we heard from Rand Fishkin, cofounder of SEOMoz, who had $24 million taken back after term sheets were signed.

Fishkin says “everything was signed” with his investor in August

Read more: http://www.businessinsider.com/vcs-money-drying-up-2011-8?utm_source=Triggermail&utm_medium=email&utm_term=10+Things+In+Tech+You+Need+To+Know&utm_campaign=Post+Blast+%28sai%29:+10+Things+You+Need+To+Know+This+Morning#ixzz1X1sq9ZeI

People tend not to note the non-binding nature of term sheets – non-binding on one side.