14,112 research outputs found
Approaching the Coverability Problem Continuously
The coverability problem for Petri nets plays a central role in the
verification of concurrent shared-memory programs. However, its high
EXPSPACE-complete complexity poses a challenge when encountered in real-world
instances. In this paper, we develop a new approach to this problem which is
primarily based on applying forward coverability in continuous Petri nets as a
pruning criterion inside a backward coverability framework. A cornerstone of
our approach is the efficient encoding of a recently developed polynomial-time
algorithm for reachability in continuous Petri nets into SMT. We demonstrate
the effectiveness of our approach on standard benchmarks from the literature,
which shows that our approach decides significantly more instances than any
existing tool and is in addition often much faster, in particular on large
instances.Comment: 18 pages, 4 figure
How to Integrate a Polynomial over a Simplex
This paper settles the computational complexity of the problem of integrating
a polynomial function f over a rational simplex. We prove that the problem is
NP-hard for arbitrary polynomials via a generalization of a theorem of Motzkin
and Straus. On the other hand, if the polynomial depends only on a fixed number
of variables, while its degree and the dimension of the simplex are allowed to
vary, we prove that integration can be done in polynomial time. As a
consequence, for polynomials of fixed total degree, there is a polynomial time
algorithm as well. We conclude the article with extensions to other polytopes,
discussion of other available methods and experimental results.Comment: Tables added with new experimental results. References adde
A programing system for research and applications in structural optimization
The flexibility necessary for such diverse utilizations is achieved by combining, in a modular manner, a state-of-the-art optimization program, a production level structural analysis program, and user supplied and problem dependent interface programs. Standard utility capabilities in modern computer operating systems are used to integrate these programs. This approach results in flexibility of the optimization procedure organization and versatility in the formulation of constraints and design variables. Features shown in numerical examples include: variability of structural layout and overall shape geometry, static strength and stiffness constraints, local buckling failure, and vibration constraints
Parallelization of dynamic programming recurrences in computational biology
The rapid growth of biosequence databases over the last decade has led to a performance bottleneck in the applications analyzing them. In particular, over the last five years DNA sequencing capacity of next-generation sequencers has been doubling every six months as costs have plummeted. The data produced by these sequencers is overwhelming traditional compute systems. We believe that in the future compute performance, not sequencing, will become the bottleneck in advancing genome science. In this work, we investigate novel computing platforms to accelerate dynamic programming algorithms, which are popular in bioinformatics workloads. We study algorithm-specific hardware architectures that exploit fine-grained parallelism in dynamic programming kernels using field-programmable gate arrays: FPGAs). We advocate a high-level synthesis approach, using the recurrence equation abstraction to represent dynamic programming and polyhedral analysis to exploit parallelism. We suggest a novel technique within the polyhedral model to optimize for throughput by pipelining independent computations on an array. This design technique improves on the state of the art, which builds latency-optimal arrays. We also suggest a method to dynamically switch between a family of designs using FPGA reconfiguration to achieve a significant performance boost. We have used polyhedral methods to parallelize the Nussinov RNA folding algorithm to build a family of accelerators that can trade resources for parallelism and are between 15-130x faster than a modern dual core CPU implementation. A Zuker RNA folding accelerator we built on a single workstation with four Xilinx Virtex 4 FPGAs outperforms 198 3 GHz Intel Core 2 Duo processors. Furthermore, our design running on a single FPGA is an order of magnitude faster than competing implementations on similar-generation FPGAs and graphics processors. Our work is a step toward the goal of automated synthesis of hardware accelerators for dynamic programming algorithms
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