Succint Solver

1
Succint Solver

• A tool for Static Analysis of Systems

2
Complex Systems are

• those whose properties are not fully explained
  by an understanding of its component parts.1

Climate, finance, www, molecular networks within
cells are some of them.
3
Knowing more and moreabout less and less

• Shortfalls in reductionism are increasingly
  apparent
• Information overload
• An example the gene for syndrome

4
Reductionist Approach

• Physical chemistry can be understood in terms of
  atomic physics
• Cell biology in terms of how biomolecules work
• Organisms in terms of how their component cell
  system interact
• Software development in terms of integration of
  objects.

5
Functionality

• Knowledge no more from the structures but from
  the functions these components have in the
  dynamic evolution of systems

Knowledge
Production
Organization
Structure must be related to behavior
6
Complexity
Since the amount of data available on the
structure is huge, we can easily infer that we
need smart techniques to investigate the dynamic
properties the behavior or evolution 3
7
Agenda

• Static Analysis
• Succint Solver
• ALFP Alternation-free fragment of Least Fixed
  Point Logic
• Ambient-Calculi Languages
• Data Structures for an application

8
STATIC ANALYSIS
9
Hallmark the ability

• to statically extract complex information about
  the dynamic behavior of programs by
• executing the programs, by simulation
• systematic inspecting the program text

10
Origin and Extensions

• Compiler optimization, to handle large programs
• Validation of safety and security properties of
  programs and systems
• Applications in Systems Biology

11
Vantages x Disadvantages

• The information extracted from a program is
  guaranteed to be a correct description of the
  behavior of the program.

• For most interesting properties it is impossible
  to obtain exact information so typically static
  analysis are approximative.

12
The nature of approximation
universe
exact answer
over-approx.
Over-approximation
The exact word
unacceptable
Under-approximation
Unacceptable situation
13
Over-approximation

universe
exact answer
over-approx.

• When we have an over-approximation to the exact
  behavior of a program we can guarantee the
  certain events will never happen namely those
  not included in the analysis result.

14
Under-approximation

• When we have an under-approximation to the exact
  behavior of a program we can guarantee the
  certain events will indeed happen namely those
  included in the analysis result.

exact answer
universe
15
Approximations of the possible evolution of
systems

• Efficiency

• Precision of the analysis

The more precision we require the more costly
will the implementation be.
16
SUCCINT SOLVER
17
Specification

• The Succint Solver is implemented using NJ/SML
  featured with modular structures, continuation
  and memoizations.
• Control Flow Analysis

18
ALFP Alternation-free Least Fixed Point Logic
19
Syntax

• Assume we are given a fixed countable set X of
  (auxiliary) variables and a finite ranked
  alphabet R of predicate symbols. Then the set of
  clauses, cl is given by the following grammar
• where R ? R is a k-ary predicate symbol
• for k ?1, x, x1, ? X denote arbitrary
  variables
• 1 is the always true clause. Queries and negative
  queries R() and R(), whereas the other
  occurrences are called assertions of the
  predicate R.

20
Semantics
21
Dealing with negations

• Restriction to alternation-free formulas
• Notion of stratification
• A clause is an ALFP if it has the form
• and there is a function rank R ?IN such that for
  all j1,,k, the following properties hold
• all predicates of assertions in clj have rank j
• all predicates of queries in clj have ranks at
  most j
• all predicates of negated queries in clj have
  ranks strictly less than j.

cl cl1 ? ? clk
22
Satisfaction relations

• Given a non-empty and countable universe U of
  atomic values together with interpretations p and
  o for predicate symbols and free variables
  respectively, the satisfaction relations are
• for pre-conditions and clauses showed in the
  previous table.
• ?(R) set of k-tuples (a1, , ak) from U
  associated with the k-ary predicate R
• ?(x) for the atom of U bound to x
• ?x?a stands for the mapping that is as ?
  except that x is mapped to a.

23
Free variables

• In the sequel we view the free variables
  occurring in a formula as constant symbols or
  atoms from the finite universe U. Thus, given an
  interpretation ?0 of the constant symbols, in the
  clause cl, we call an interpretation ? of the
  predicate symbols R a solution to the clause
  provided

24
Polinomial Time

• The solution of an ALFP clause can be found in
  polynomial time in the size of the universe i.e.
  in the number of groups and capabilities
• This complexity is due to a generalization of a
  meta-complexity result for Horn Clause 7, which
  states that
• The time needed to compute a solution is
  asymptotically the same as the time needed to
  check the validity of an estimate
• The degree of the complexity polynomial is
  dominated by one plus the nesting depth of
  quantifiers occurring in the clause.

25
Succint Solver an example in Discretionary
Ambients
26
Ambient-Calculi Languages
27
Mobile Ambients
28
Discretionary Ambients
29
Discretionary Ambients
30
Discretionary Ambients
31
BioAmbients
Have a look at the blackboard!
32
Contexts
There is no only interaction but movement of
entities that create another barrier to the
studies of the dynamism of the systems 0CFA The
computation of the over-aproximation to the
father-son relationship between ambients and
capabilities and in doing so it ignores the order
in which the capabilities are executed and also
it does not take the context in account. 1CFA It
is an over-aproximation where the grandfather
information is consistent in order to father-son
relationship to be updated. kCFA The semantics
requires that all ancestors of the two components
involved in an action are consistent. Actual step
of the research construction of this
generalization.
33
Data structures for an application
34
Program SML code
Signal transduction pathway example
local (----------------------------------
composition of Gene_A ------) val kin
Amb("KINASE", SumPre(SibO("bb2",
"ptail"), Nill),
Pre(ChildI("bb3", "d"),
Nil) val pra
Amb("PROTEIN_A", Par
Pre(Exit("b"),
Pre(Accept("tf"),
SumSumPre(ChildI("bb1", "d"), Nill),
Pre(Expel("g"),
Pre(SibO("degp", "d"),
Pre(ChildI("bb3", "d"),
Pre(ChildI("bb3", "d"),
Nil)))) ,
Pre(SibO("degp", "d"),
Pre(ChildI("bb3", "d"),
Nil)) )) ,kin
35
Analysis Result
36
Summary

• We have learned that tools for static analysis of
  programs have been applied to learn about the
  dynamic behavior of complex systems.
• An innovation is their applicability in Systems
  Biology since we believe to be very close of the
  language which model the nature BioAmbients -
  we can create programs (prototypes /
  experimentation, for biologists)
• The results of this kind of analysis are
  approximatives but the properties that we can
  investigate for systems can be an order of
  magnitude larger than the ones that we can handle
  with dynamic tools
• To build models-prototypes and to perform static
  analysis on them these will be the steps of the
  computer scientists to reveal the behavior of
  Complex Systems, in the most varied areas.
• While studding the language of the nature we are
  improving the knowledge about the language of
  artificial systems too.

37
Where to get more information

• 1 Gallagher, R. and Appenzeller, T. Beyond
  Reductionism. Science, vol 284, 1999, 79.
• 2 C. Hankin, Hanne Riis Nielson and Flemming
  Nielson. Principles of Programming Analysis .
  Springer, 1999.
• 3 Debora Schuch da Rosa, Corrado Priami, Hanne
  Riis Nielson and Flemming Nielson. Static
  Analysis for Systems Biology. Work in progress,
  2003.
• 4 Mikael Buchholtz, Hanne Riis Nielson and
  Flemming Nielson. Experiments with Succint
  Solvers . February 12, 2002. SECSAFE-IMM-002. (
  .pdf)
• 5 Hongyan Sun, Hanne Riis Nielson and Flemming
  Nielson. Data Structures in the Succint Solver .
  November 11, 2002. SECSAFE IMM-005 (.pdf)

38
More references

• 6 Lewin, Roger. Complexity Life at the edge of
  chaos. The University of Chicago Press, 2nd ed.,
  1999.
• 7 McAllester. On the complexity analysis of
  static analysis. In Static Analysis, 6th
  International Symposium, SAS 1999, vol 1694 of
  LNCS, pages 312-329. Springer, 1999.

39
Contacts

• schuch_at_dit.unitn.it
• Bioinformatics lab
• ICT-UNITN