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Boolean Algebra with Presburger Arithmetic (BAPA) is a decidable logic that can express constraints on sets of elements and their cardinalities. Problems from verification of complex properties of software often contain fragments that belong to quantifier- ...
Techniques such as verification condition generation, predicate abstraction, and expressive type systems reduce software verification to proving formulas in expressive logics. Programs and their specifications often make use of data structures such as sets ...
The efficient synthesis of circuits is a well-studied problem. Due to the NP-hardness of the problem, no optimal algorithm has been presented so far. However, the heuristics presented by several researchers in the past, which are also adopted by commercial ...
For more than 35 years, the fastest known method for integer multiplication has been the Schonhage-Strassen algorithm running in time O(n log n log log n). Under certain restrictive conditions, there is a corresponding Omega(n log n) lower bound. All this ...
We explore the problem of automated reasoning about the non-disjoint combination of logics that share set variables and operations. We prove a general combination theorem, and apply it to show the decidability for the quantifier-free combination of formula ...
The segmentation of Drosophila is a prime model to study spatial patterning during embryogenesis. The spatial expression of segment polarity genes results from a complex network of interacting proteins whose expression products are maintained after success ...
Motivated by applications in software verification, we explore automated reasoning about the non-disjoint combination of theories of infinitely many finite structures, where the theories share set variables and set operations. We prove a combination theore ...
Deciding consistency of constraint networks is a fundamental problem in qualitative spatial and temporal reasoning. In this paper we introduce a divide-and-conquer method that recursively partitions a given problem into smaller sub-problems in deciding con ...
Let C be a family of n convex bodies in the plane, which can be decomposed into k subfamilies of pairwise disjoint sets. It is shown that the number of tangencies between the members of C is at most O(kn), and that this bound cannot be improved. If we only ...
Modern experimental techniques for the quantitative, time-course measurement of protein concentrations and gene activation levels enable the identification of dynamical models of genetic regulatory networks. In general, identification involves fitting appr ...
