Semi-regular sequences over F2 are sequences of homogeneous elements of the algebra B (n) = F2[X1, ..., Xn]/(X 2 1 , ..., X 2 n ), which have as few relations between them as possible. It is believed that most such systems are F2-semi-regular and this property has important consequences for understanding the complexity of Gröbner basis algorithms such as F4 and F5 for solving such systems. In fact even in one of the simplest and most important cases, that of quadratic sequences of length n in n

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... variables, the question of the existence of semi-regular sequences for all n remains open. In this paper we present a new framework for the concept of F2-semi-regularity which we hope will allow the use of ideas and machinery from homological algebra to be applied to this interesting and important open question. First we introduce an analog of the Koszul complex and show that F2-semi-regularity can be characterized by the exactness of this complex. We show how the well known formula for the Hilbert series of a F2-semi-regular sequence can be deduced from the Koszul complex. Finally we show that the concept of first fall degree also has a natural description in terms of the Koszul complex.