This paper presents algorithms for the automatic synthesis of real-time controllers by finding a winning strategy for certain games defined by the timed-automata of Alur and Dill. In such games, the outcome depends on the players' actions as well as on their timing. We believe that these results will pave the way for the application of program synthesis techniques to the construction of real-time embedded systems from their specifications.

On the synthesis of discrete controllers for timed systems

Many compiler optimization techniques depend on the ability to calculate the number of elements that satisfy certain conditions. If these conditions can be represented by linear constraints, then such problems are equivalent to counting the number of integer points in (possibly) parametric polytopes. It is well known that the enumerator of such a set can be represented by an explicit function consisting of a set of quasi-polynomials, each associated with a chamber in the parameter space. Previously, interpolation was used to obtain these quasi-polynomials, but this technique has several disadvantages. Its worst-case computation time for a single quasi-polynomial is exponential in the input size, even for fixed dimensions. The worst-case size of such a quasi-polynomial (measured in bits needed to represent the quasi-polynomial) is also exponential in the input size. Under certain conditions this technique even fails to produce a solution. Our main contribution is a novel method for calculating the required quasi-polynomials analytically. It extends an existing method, based on Barvinok's decomposition, for counting the number of integer points in a non-parametric polytope. Our technique always produces a solution and computes polynomially-sized enumerators in polynomial time (for fixed dimensions).

/pdf/counting-integer-points-in-parametric-polytopes-using-5bdmkmz47i.pdf

Counting Integer Points in Parametric Polytopes Using Barvinok's Rational Functions

We study the problem of automatically analyzing the worst-case resource usage of procedures with several arguments. Existing automatic analyses based on amortization or sized types bound the resource usage or result size of such a procedure by a sum of unary functions of the sizes of the arguments.In this article we generalize this to arbitrary multivariate polynomial functions thus allowing bounds of the form mn which had to be grossly overestimated by m2 p n2 before. Our framework even encompasses bounds like ∑i,j≤ n mi mj where the mi are the sizes of the entries of a list of length n.This allows us for the first time to derive useful resource bounds for operations on matrices that are represented as lists of lists and to considerably improve bounds on other superlinear operations on lists such as longest common subsequence and removal of duplicates from lists of lists. Furthermore, resource bounds are now closed under composition which improves accuracy of the analysis of composed programs when some or all of the components exhibit superlinear resource or size behavior.The analysis is based on a novel multivariate amortized resource analysis. We present it in form of a type system for a simple first-order functional language with lists and trees, prove soundness, and describe automatic type inference based on linear programming.We have experimentally validated the automatic analysis on a wide range of examples from functional programming with lists and trees. The obtained bounds were compared with actual resource consumption. All bounds were asymptotically tight, and the constants were close or even identical to the optimal ones.

Multivariate amortized resource analysis

The continued development of efficient automated decision procedures has spurred the resurgence of research on symbolic execution over the past decade. Researchers have applied symbolic execution to a wide range of software analysis problems including: checking programs against contract specifications, inferring bounds on worst-case execution performance, and generating path-adequate test suites for widely used library code. In this paper, we explore the adaptation of symbolic execution to perform a more quantitative type of reasoning --- the calculation of estimates of the probability of executing portions of a program. We present an extension of the widely used Symbolic PathFinder symbolic execution system that calculates path probabilities. We exploit state-of-the-art computational algebra techniques to count the number of solutions to path conditions, yielding exact results for path probabilities. To mitigate the cost of using these techniques, we present two optimizations, PC slicing and count memoization, that significantly reduce the cost of probabilistic symbolic execution. Finally, we present the results of an empirical evaluation applying our technique to challenging library container implementations and illustrate the benefits that adding probabilities to program analyses may offer.

Probabilistic symbolic execution

We study the problem of automatically analyzing the worst-case resource usage of procedures with several arguments. Existing automatic analyses based on amortization, or sized types bound the resource usage or result size of such a procedure by a sum of unary functions of the sizes of the arguments.In this paper we generalize this to arbitrary multivariate polynomial functions thus allowing bounds of the form mn which had to be grossly overestimated by m2+n2 before. Our framework even encompasses bounds like ∗i,j≤n m_i mj where the mi are the sizes of the entries of a list of length n.This allows us for the first time to derive useful resource bounds for operations on matrices that are represented as lists of lists and to considerably improve bounds on other super-linear operations on lists such as longest common subsequence and removal of duplicates from lists of lists.Furthermore, resource bounds are now closed under composition which improves accuracy of the analysis of composed programs when some or all of the components exhibit super-linear resource or size behavior.The analysis is based on a novel multivariate amortized resource analysis. We present it in form of a type system for a simple first-order functional language with lists and trees, prove soundness, and describe automatic type inference based on linear programming.We have experimentally validated the automatic analysis on a wide range of examples from functional programming with lists and trees. The obtained bounds were compared with actual resource consumption. All bounds were asymptotically tight, and the constants were close or even identical to the optimal ones.

/pdf/multivariate-amortized-resource-analysis-4012ybwhix.pdf

This work presents a technique to compute symbolic polynomial approximations of the amount of dynamic memory required to safely execute a method without running out of memory, for Javalike imperative programs. We consider object allocations and deallocations made by the method and the methods it transitively calls. More precisely, given an initial configuration of the stack and the heap, the peak memory consumption is the maximum space occupied by newly created objects in all states along a run from it. We over-approximate the peak memory consumption using a scopedmemory management where objects are organized in regions associated with the lifetime of methods. We model the problem of computing the maximum memory occupied by any region configuration as a parametric polynomial optimization problem over a polyhedral domain and resort to Bernstein basis to solve it. We apply the developed tool to several benchmarks.

Parametric prediction of heap memory requirements

We present a static analysis for computing a parametric upper-bound of the amount of memory dynamically allocated by (Java-like) imperative object-oriented programs. We propose a general procedure for synthesizing non-linear formulas which conservatively estimate the quantity of memory explicitly allocated by a method as a function of its parameters. We have implemented the procedure and evaluated it on several benchmarks. Experimental results produced exact estimations for most test cases, and quite precise approximations for many of the others. We also apply our technique to compute usage in the context of scoped memory and discuss some open issues.

/pdf/a-static-analysis-for-synthesizing-parametric-specifications-13jxc8n6qw.pdf

A Static Analysis for Synthesizing Parametric Specifications of Dynamic Memory Consumption.

We present a new scheduler architecture, which permits adding QoS (quality of service) policies to the scheduling decisions. We also present a new scheduling synthesis method which allows a designer to obtain a safe scheduler for a particular application. Our scheduler architecture and scheduler synthesis method can be used for heterogeneous applications where the tasks communicate through various synchronization primitives. We present a prototype implementation of this scheduler architecture and related mechanisms on top of an open-source OS (operating system) for embedded systems.

/pdf/synthesis-of-safe-qos-extendible-application-specific-1qm0yik9zh.pdf

Synthesis of safe, QoS extendible, application specific schedulers for heterogeneous real-time systems

http://www.runtime-verification.org/rv2004/papers/paper07.pdf

Program Instrumentation and Run-Time Analysis of Scoped Memory in Java

https://hal.inria.fr/inria-00602874/document

Sergio Yovine

Papers

Parametric prediction of heap memory requirements

A Static Analysis for Synthesizing Parametric Specifications of Dynamic Memory Consumption.

Synthesis of safe, QoS extendible, application specific schedulers for heterogeneous real-time systems

Program Instrumentation and Run-Time Analysis of Scoped Memory in Java

Fast Escape Analysis for Region-based Memory Management