Proceedings Work-In-Progress Session of the 13th Real-Time and Embedded Technology and Applications Symposium

The Work-In-Progress session of the 13th IEEE Real-Time and Embedded Technology and Applications Symposium (RTAS\u2707) presents papers describing contributions both to state of the art and state of the practice in the broad field of real-time and embedded systems. The 17 accepted papers were selected from 19 submissions. This proceedings is also available as Washington University in St. Louis Technical Report WUCSE-2007-17, at http://www.cse.seas.wustl.edu/Research/FileDownload.asp?733. Special thanks go to the General Chairs – Steve Goddard and Steve Liu and Program Chairs - Scott Brandt and Frank Mueller for their support and guidance

The Reachability Problem for Petri Nets is Not Elementary

Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. Decidability was proved by Mayr in his seminal STOC 1981 work, and the currently best published upper bound is non-primitive recursive Ackermannian of Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound, i.e. that the reachability problem needs a tower of exponentials of time and space. Until this work, the best lower bound has been exponential space, due to Lipton in 1976. The new lower bound is a major breakthrough for several reasons. Firstly, it shows that the reachability problem is much harder than the coverability (i.e., state reachability) problem, which is also ubiquitous but has been known to be complete for exponential space since the late 1970s. Secondly, it implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi and other areas, that are known to admit reductions from the Petri nets reachability problem, are also not elementary. Thirdly, it makes obsolete the currently best lower bounds for the reachability problems for two key extensions of Petri nets: with branching and with a pushdown stack.Comment: Final version of STOC'1

The reachability problem for Petri nets is not elementary

Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. Decidability was proved by Mayr in his seminal STOC 1981 work, and the currently best published upper bound is non-primitive recursive Ackermannian of Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound, i.e. that the reachability problem needs a tower of exponentials of time and space. Until this work, the best lower bound has been exponential space, due to Lipton in 1976. The new lower bound is a major breakthrough for several reasons. Firstly, it shows that the reachability problem is much harder than the coverability (i.e., state reachability) problem, which is also ubiquitous but has been known to be complete for exponential space since the late 1970s. Secondly, it implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi and other areas, that are known to admit reductions from the Petri nets reachability problem, are also not elementary. Thirdly, it makes obsolete the currently best lower bounds for the reachability problems for two key extensions of Petri nets: with branching and with a pushdown stack

The reachability problem for petri nets is not elementary

Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modeling and analysis of hardware, software, and database systems, as well as chemical, biological, and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. Decidability was proved by Mayr in his seminal STOC 1981 work, and, currently, the best published upper bound is non-primitive recursive Ackermannian of Leroux and Schmitz from Symposium on Logic in Computer Science 2019. We establish a non-elementary lower bound, i.e., that the reachability problem needs a tower of exponentials of time and space. Until this work, the best lower bound has been exponential space, due to Lipton in 1976. The new lower bound is a major breakthrough for several reasons. Firstly, it shows that the reachability problem is much harder than the coverability (i.e., state reachability) problem, which is also ubiquitous but has been known to be complete for exponential space since the late 1970s. Secondly, it implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi, and other areas, which are known to admit reductions from the Petri nets reachability problem, are also not elementary. Thirdly, it makes obsolete the current best lower bounds for the reachability problems for two key extensions of Petri nets: with branching and with a pushdown stack

Memory Optimizations for Time-Predictable Embedded Software

Ph.DDOCTOR OF PHILOSOPH

Vector addition systems and their applications in the verification of computer programs

Vector Addition Systems (and, equivalently, Petri nets) are a widespread formalism for modelling across a spectrum of problem domains, from logistics to hardware simulation. In this thesis, we firstly explore two classic decidability problems for these models: reachability, whether one can get to a given configuration, and coverability, whether one can exceed it. These problems are sufficent to express a wide class of verification properties for models derived from real-world use cases, including safety and deadlock-freeness. We present and implement a number of approaches for solving both the coverability and reachability problems, including KReach, the first known implementation of a complete decider for the general Petri net reachability problem. Petri nets offer a natural model of concurrent processes and one of the most common modern use cases for the model is in the verification of safety properties for software, especially sofware with concurrency. In the later half of this work we address some approaches to deciding properties of programs written in Finitary Idealized Concurrent Algol (FICA), a prototypical language combining functional, imperative, and higher-order concurrent programming. We introduce a new family of “leafy” automata models, all based on a novel representation of internal configurations as a tree structure whose semantics is inspired by game-semantic interpretations of FICA terms. We give translations from such terms to our automata and across the work derive decidability of some useful properties for successively more expressive subsets of terms, using a variety of methods including via reachability on Petri nets. We believe these models will help to unify the game- and automata-theoretic views of programming languages and provide a useful basis on which to further study the theory of concurrency