Pushing the envelope of Optimization Modulo Theories with Linear-Arithmetic Cost Functions

In the last decade we have witnessed an impressive progress in the expressiveness and efficiency of Satisfiability Modulo Theories (SMT) solving techniques. This has brought previously-intractable problems at the reach of state-of-the-art SMT solvers, in particular in the domain of SW and HW verification. Many SMT-encodable problems of interest, however, require also the capability of finding models that are optimal wrt. some cost functions. In previous work, namely "Optimization Modulo Theory with Linear Rational Cost Functions -- OMT(LAR U T )", we have leveraged SMT solving to handle the minimization of cost functions on linear arithmetic over the rationals, by means of a combination of SMT and LP minimization techniques. In this paper we push the envelope of our OMT approach along three directions: first, we extend it to work also with linear arithmetic on the mixed integer/rational domain, by means of a combination of SMT, LP and ILP minimization techniques; second, we develop a multi-objective version of OMT, so that to handle many cost functions simultaneously; third, we develop an incremental version of OMT, so that to exploit the incrementality of some OMT-encodable problems. An empirical evaluation performed on OMT-encoded verification problems demonstrates the usefulness and efficiency of these extensions.Comment: A slightly-shorter version of this paper is published at TACAS 2015 conferenc

On Optimization Modulo Theories, MaxSMT and Sorting Networks

Optimization Modulo Theories (OMT) is an extension of SMT which allows for finding models that optimize given objectives. (Partial weighted) MaxSMT --or equivalently OMT with Pseudo-Boolean objective functions, OMT+PB-- is a very-relevant strict subcase of OMT. We classify existing approaches for MaxSMT or OMT+PB in two groups: MaxSAT-based approaches exploit the efficiency of state-of-the-art MAXSAT solvers, but they are specific-purpose and not always applicable; OMT-based approaches are general-purpose, but they suffer from intrinsic inefficiencies on MaxSMT/OMT+PB problems. We identify a major source of such inefficiencies, and we address it by enhancing OMT by means of bidirectional sorting networks. We implemented this idea on top of the OptiMathSAT OMT solver. We run an extensive empirical evaluation on a variety of problems, comparing MaxSAT-based and OMT-based techniques, with and without sorting networks, implemented on top of OptiMathSAT and {\nu}Z. The results support the effectiveness of this idea, and provide interesting insights about the different approaches.Comment: 17 pages, submitted at Tacas 1

Correct composition of dephased behavioural models

This research is supported by EPSRC grant EP/M014290/1.Scenarios of execution are commonly used to specify partial behaviour and interactions between different objects and components in a system. To avoid overall inconsistency in specifications, various automated methods have emerged in the literature to compose (behavioural) models. In recent work, we have shown how the theorem prover Isabelle can be combined with the constraint solver Z3 to efficiently detect inconsistencies in two or more behavioural models and, in their absence, generate the composition. Here, we extend our approach further and show how to generate the correct composition (as a set of valid traces) of dephased models. This work has been inspired by a problem from a medical domain where different care pathways (for chronic conditions) may be applied to the same patient with different starting points.Postprin

Noise-Adaptive Compiler Mappings for Noisy Intermediate-Scale Quantum Computers

A massive gap exists between current quantum computing (QC) prototypes, and the size and scale required for many proposed QC algorithms. Current QC implementations are prone to noise and variability which affect their reliability, and yet with less than 80 quantum bits (qubits) total, they are too resource-constrained to implement error correction. The term Noisy Intermediate-Scale Quantum (NISQ) refers to these current and near-term systems of 1000 qubits or less. Given NISQ's severe resource constraints, low reliability, and high variability in physical characteristics such as coherence time or error rates, it is of pressing importance to map computations onto them in ways that use resources efficiently and maximize the likelihood of successful runs. This paper proposes and evaluates backend compiler approaches to map and optimize high-level QC programs to execute with high reliability on NISQ systems with diverse hardware characteristics. Our techniques all start from an LLVM intermediate representation of the quantum program (such as would be generated from high-level QC languages like Scaffold) and generate QC executables runnable on the IBM Q public QC machine. We then use this framework to implement and evaluate several optimal and heuristic mapping methods. These methods vary in how they account for the availability of dynamic machine calibration data, the relative importance of various noise parameters, the different possible routing strategies, and the relative importance of compile-time scalability versus runtime success. Using real-system measurements, we show that fine grained spatial and temporal variations in hardware parameters can be exploited to obtain an average $2.9$x (and up to $18$x) improvement in program success rate over the industry standard IBM Qiskit compiler.Comment: To appear in ASPLOS'1