Efficient computation of exact solutions for quantitative model checking

Efficient computation of exact solutions for quantitative model checking

Quantitative model checkers for Markov Decision Processes typically use finite-precision arithmetic, since exact techniques are generally too expensive or limited in scalability. In this paper we propose a method for obtaining exact results starting from an approximated solution in finite-precision arithmetic. The input of the method is a description of a scheduler, which can be obtained by a m...

Exact Solutions of Holonomic Quantum Computation

Holonomic quantum computation is analyzed from geometrical viewpoint. We develop an optimization scheme in which an arbitrary unitary gate is implemented with a small circle in a complex projective space. Exact solutions for the Hadamard, CNOT and 2-qubit discrete Fourier transformation gates are explicitly constructed.

Efficient Computation of Exact IRV Margins

The margin of victory is easy to compute for many election schemes but difficult for Instant Runoff Voting (IRV). This is important because arguments about the correctness of an election outcome usually rely on the size of the electoral margin. For example, risk-limiting audits require a knowledge of the margin of victory in order to determine how much auditing is necessary. This paper presents...

Efficient exact computation of iterated maps

Quantitative Model checking

We present QMC, a one-sided error Monte Carlo decision procedure for the LTL model-checking problem S |= φ. Besides serving as a randomized algorithm for LTL model checking, QMC delivers quantitative information about the likelihood that S |= φ. In particular, given a specification S of a finite-state system, an LTL formula φ, and parameters and δ, QMC performs random sampling to compute an est...