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New developments in the theory of Gröbner bases and applications to formal verification. (English) Zbl 1164.68019
Summary: We present foundational work on standard bases over rings and on Boolean Gröbner bases in the framework of Boolean functions. The research was motivated by our collaboration with electrical engineers and computer scientists on problems arising from formal verification of digital circuits. In fact, algebraic modelling of formal verification problems is developed on the word-level as well as on the bit-level. The word-level model leads to Gröbner bases in the polynomial ring over $$\mathbb Z/2^n$$ while the bit-level model leads to Boolean Gröbner bases. In addition to the theoretical foundations of both approaches, the algorithms have been implemented. Using these implementations we show that special data structures and the exploitation of symmetries make Gröbner bases competitive to state-of-the-art tools from formal verification but having the advantage of being systematic and more flexible.

##### MSC:
 68Q60 Specification and verification (program logics, model checking, etc.) 06E30 Boolean functions 13F20 Polynomial rings and ideals; rings of integer-valued polynomials 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 68W30 Symbolic computation and algebraic computation 94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
##### Software:
CoCoA; CUDD; Macaulay2; MiniSat; PolyBoRi; SageMath; SATLIB; SINGULAR; slimgb
Full Text:
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