</a>Polyhedral patterns: representation of complex numerical abstractions

Polyhedral Empowerment of Networks through Symmetry: psycho-social implications for organization and global governance (Part #12)

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As a consequence of the computer-related developments above, a polyhedral pattern library has been instigated by Roberto Bagnara at the University of Parma (Roberto Bagnara, Convex Polyhedra for the Analysis and Verification of Hardware and Software Systems: the "Parma Polyhedra Library", 2003; Roberto Bagnara et al., The PPL: A Library for Representing Numerical Abstractions: Current and Future Plans, 2004).

The Parma Polyhedra Library (PPL) is a modern and reasonably complete library providing numerical abstractions especially targeted at applications in the field of analysis and verification of complex systems. The PPL can handle all the convex polyhedra that can be defined as the intersection of a finite number of (open or closed) hyperspaces, each described by an equality or inequality (strict or non-strict) with rational coefficients. The PPL also handles restricted classes of polyhedra that offer interesting complexity/precision tradeoffs. The library also supports finite powersets of (any kind of) polyhedra and linear programming problems solved with an exact-arithmetic version of the simplex algorithm.

As highlighted by the PPL (The Parma Polyhedra Library), justifications for the creation of such a library include:

• programs need to be designed, developed and maintained over their entire lifespan (up to 20 and more years) at reasonable costs;
• programs have exploded in size over the last 25 years so that more and more with tens of millions of lines of code are in general use;
• unassisted development and maintenance teams do not stand a chance to follow such an explosion in size and complexity;
• the problem of software reliability is one of the most important problems computer science has to face;
• this justifies the growing interest in mechanical tools to help the programmer reasoning about programs.
• the large number of bugs in much of software is becoming intolerable, even in office applications, but highly publicized examples include:.
  • the Mars Climate Orbiter burned in the martian atmosphere in 1999 after missing its orbit insertion because unit computations were inconsistent. The same year, Mars Polar Lander is suspected of having crashed on Mars upon landing when a software tag was not reset properly.
  • in the 1997 Mars Pathfinder (MPF) technology demonstration mission, a day's exploration time was lost when ground support teams were forced to reboot the system while downloading science data.
  • NASA's 2003 Mars Exploration Rover (MER) mission includes two rovers. At a cost of $400 million for each rover, a coding error that shuts down a rover overnight would in effect be a $4.4 million mistake, as well as a loss of valuable exploration time on the planet.

Again the question is on what range of polyhedral patterns is psycho-social organization currently based and whether much of relevance could be enabled by extending that range. Does the restriction of the range considered credible result in what Magoroh Maruyama has termed "subunderstanding" (Polyocular Vision or Subunderstanding, 2004)? In his terms is "polyocular" ensured by "polyhedral"?

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