Generating invariants for non-linear loops by linear algebraic methods
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| 024 | 7 | 0 | |a 10.1007/s00165-015-0333-3 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00165-015-0333-3 | ||
| 245 | 0 | 0 | |a Generating invariants for non-linear loops by linear algebraic methods |h [Elektronische Daten] |c [Rachid Rebiha, Arnaldo Moura, Nadir Matringe] |
| 520 | 3 | |a We present new computational methods that can automate the discovery and the strengthening of non-linear interrelationships among the variables of programs containing non-linear loops, that is, that give rise to multivariate polynomial and fractional relationships. Our methods have complexities lower than the mathematical foundations of the previous approaches, which used Gröbner basis computations, quantifier eliminations or cylindrical algebraic decompositions. We show that the preconditions for discrete transitions can be viewed as morphisms over a vector space of degree bounded by polynomials. These morphisms can, thus, be suitably represented by matrices. We also introduce fractional and polynomial consecution, as more general forms for approximating consecution. The new relaxed consecution conditions are also encoded as morphisms represented by matrices. By so doing, we can reduce the non-linear loop invariant generation problem to the computation of eigenspaces of specific morphisms. Moreover, as one of the main results, we provide very general sufficient conditions allowing for the existence and computation of whole loop invariant ideals. As far as it is our knowledge, it is the first invariant generation methods that can handle multivariate fractional loops. | |
| 540 | |a British Computer Society, 2015 | ||
| 690 | 7 | |a Formal methods |2 nationallicence | |
| 690 | 7 | |a Invariant generation |2 nationallicence | |
| 690 | 7 | |a Linear algebra |2 nationallicence | |
| 700 | 1 | |a Rebiha |D Rachid |u Institute of Computing, University of Campinas, Campinas, Brazil |4 aut | |
| 700 | 1 | |a Moura |D Arnaldo |u Institute of Computing, University of Campinas, Campinas, Brazil |4 aut | |
| 700 | 1 | |a Matringe |D Nadir |u LMA, University of Poitiers, Poitiers, France |4 aut | |
| 773 | 0 | |t Formal Aspects of Computing |d Springer London |g 27/5-6(2015-11-01), 805-829 |x 0934-5043 |q 27:5-6<805 |1 2015 |2 27 |o 165 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00165-015-0333-3 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00165-015-0333-3 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Rebiha |D Rachid |u Institute of Computing, University of Campinas, Campinas, Brazil |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Moura |D Arnaldo |u Institute of Computing, University of Campinas, Campinas, Brazil |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Matringe |D Nadir |u LMA, University of Poitiers, Poitiers, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Formal Aspects of Computing |d Springer London |g 27/5-6(2015-11-01), 805-829 |x 0934-5043 |q 27:5-6<805 |1 2015 |2 27 |o 165 | ||