zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Verifying invariants by approximate image computation. (English) Zbl 0907.68121
Moller, Faron (ed.), Verification of infinite state systems, Infinity ’97. Selected papers from the 2nd international workshop, Bologna, Italy, July 11–12, 1997. Amsterdam: Elsevier, Electronic Notes in Theoretical Computer Science. 9, 13 p. (1997).
Summary: Automatic formal verification of safety properties typically requires computing reachable states of a system. A more efficient (and less automatic) alternative is to check whether a user suggested superset of reachable states is an invariant, i.e. whether it contains its image specified by the transition relation of the system. Still, this approach may be prohibitively expensive due to the complexity of image computation. To alleviate this problem we suggest to use approximate image computations, and we show that even though the approximation computes a superset of the image, it can, in certain cases, be used to answer categorically the question whether the suggested invariant contains its image. More precisely, we first establish sufficient conditions that the approximate image commutation and the suggested invariant need to satisfy in order to always reach a conclusive result of the verification process. Then, we use these results to show that the three approximate image computation methods proposed previously for approximate reachability analysis could be used for exact invariant verification.
MSC:
68Q60Specification and verification of programs
68U10Image processing (computing aspects)