Given a negative $D>-(log X)^{log 2-delta}$, we give a new upper bound on the number of square free integers $<X$ which are represented by some but not all forms of the genus of a primitive positive definite binary quadratic form $f$ of discriminant
$D$. We also give an analogous upper bound for square free integers of the form $q+a<X$ where $q$ is prime and $ainmathbb Z$ is fixed. Combined with the 1/2-dimensional sieve of Iwaniec, this yields a lower bound on the number of such integers $q+a<X$ represented by a binary quadratic form of discriminant $D$, where $D$ is allowed to grow with $X$ as above. An immediate consequence of this, coming from recent work of the authors in [BF], is a lower bound on the number of primes which come up as curvatures in a given primitive integer Apollonian circle packing.
Attempto Controlled English (ACE) allows domain specialists to interactively formulate requirements specifications in domain concepts. ACE can be accurately and efficiently processed by a computer, but is expressive enough to allow natural usage. The
Attempto system translates specification texts in ACE into discourse representation structures and optionally into Prolog. Translated specification texts are incrementally added to a knowledge base. This knowledge base can be queried in ACE for verification, and it can be executed for simulation, prototyping and validation of the specification.
Deriving formal specifications from informal requirements is difficult since one has to take into account the disparate conceptual worlds of the application domain and of software development. To bridge the conceptual gap we propose controlled natura
l language as a textual view on formal specifications in logic. The specification language Attempto Controlled English (ACE) is a subset of natural language that can be accurately and efficiently processed by a computer, but is expressive enough to allow natural usage. The Attempto system translates specifications in ACE into discourse representation structures and into Prolog. The resulting knowledge base can be queried in ACE for verification, and it can be executed for simulation, prototyping and validation of the specification.
Writing specifications for computer programs is not easy since one has to take into account the disparate conceptual worlds of the application domain and of software development. To bridge this conceptual gap we propose controlled natural language as
a declarative and application-specific specification language. Controlled natural language is a subset of natural language that can be accurately and efficiently processed by a computer, but is expressive enough to allow natural usage by non-specialists. Specifications in controlled natural language are automatically translated into Prolog clauses, hence become formal and executable. The translation uses a definite clause grammar (DCG) enhanced by feature structures. Inter-text references of the specification, e.g. anaphora, are resolved with the help of discourse representation theory (DRT). The generated Prolog clauses are added to a knowledge base. We have implemented a prototypical specification system that successfully processes the specification of a simple automated teller machine.
