Bisimulation equivalence of a BPP and a finite-state system can be decided in polynomial time

AbstractIn this paper we consider the problem of deciding bisimulation equivalence of a BPP and a finite-state system. We show that the problem can be solved in polynomial time and we present an algorithm deciding the problem in time O(n4). The algorithm also constructs for each state of the finite-state system a ‘symbolic’ semilinear representation of the set of all states of the BPP system which are bisimilar with this state

Bisimilarity of Pushdown Systems is Nonelementary

Given two pushdown systems, the bisimilarity problem asks whether they are bisimilar. While this problem is known to be decidable our main result states that it is nonelementary, improving EXPTIME-hardness, which was the previously best known lower bound for this problem. Our lower bound result holds for normed pushdown systems as well

On Bisimilarity of Higher-Order Pushdown Automata: Undecidability at Order Two

We show that bisimulation equivalence of order-two pushdown automata is undecidable. Moreover, we study the lower order problem of higher-order pushdown automata, which asks, given an order-k pushdown automaton and some k\u27= 2 even when the input k-PDA is deterministic and real-time

Weak Bisimulation Approximants

Bisimilarity ∼ and weak bisimilarity ≈ are canonical notions of equivalence between processes, which are defined co-inductively, but may be approached – and even reached – by their (transfinite) inductively-defined approximants ∼α and ≈α. For arbitrary processes this approximation may need to climb arbitrarily high through the infinite ordinals before stabilising. In this paper we consider a simple yet well-studied process algebra, the Basic Parallel Processes (BPP), and investigate for this class of processes the minimal ordinal α such that ≈ = ≈α. The main tool in our investigation is a novel proof of Dickson’s Lemma. Unlike classical proofs, the proof we provide gives rise to a tight ordinal bound, of ω n, on the order type of non-increasing sequences of n-tuples of natural numbers. With this we are able to reduce a long-standing bound on the approximation hierarchy for weak bisimilarity ≈ over BPP, and show that ≈ = ≈ω ω

Analysis of Probabilistic Basic Parallel Processes

Basic Parallel Processes (BPPs) are a well-known subclass of Petri Nets. They are the simplest common model of concurrent programs that allows unbounded spawning of processes. In the probabilistic version of BPPs, every process generates other processes according to a probability distribution. We study the decidability and complexity of fundamental qualitative problems over probabilistic BPPs -- in particular reachability with probability 1 of different classes of target sets (e.g. upward-closed sets). Our results concern both the Markov-chain model, where processes are scheduled randomly, and the MDP model, where processes are picked by a scheduler.Comment: This is the technical report for a FoSSaCS'14 pape

Equivalence-Checking on Infinite-State Systems: Techniques and Results

The paper presents a selection of recently developed and/or used techniques for equivalence-checking on infinite-state systems, and an up-to-date overview of existing results (as of September 2004)

Approximating Weak Bisimilarity of Basic Parallel Processes

This paper explores the well known approximation approach to decide weak bisimilarity of Basic Parallel Processes. We look into how different refinement functions can be used to prove weak bisimilarity decidable for certain subclasses. We also show their limitations for the general case. In particular, we show a lower bound of ω ∗ ω for the approximants which allow weak steps and a lower bound of ω + ω for the approximants that allow sequences of actions. The former lower bound negatively answers the open question of Jančar and Hirshfeld

Simple Equivalence Checking Tool: Deciding Bisimilarity of BPP

Import 26/06/2013Mezi standardní techniky verifikace systémů patří ověřování ekvivalencí. Ověřují se různé ekvivalence na různých modelech systému. Tato diplomová práce byla zaměřena na dva, v literatuře dostupné, algoritmy pro ověřování bisimulační ekvivalence mezi dvěma systémy specifikovanými jako základní paralelní procesy. Cílem bylo vytvoření verifikačního nástroje, který rozhodne bisimulační ekvivalenci na zadaných vstupech různých velikostí. V tomto textu je popsána tvorba tohoto nástroje včetně pojmů důležitých k pochopení použitých algoritmů. Korektnost použitých algoritmů a jejich asymptotická složitost vyplývá z citovaných zdrojů, práce se tímto nezabývá.The standard techniques of verification systems includes the verification of equivalences. On the various types of models of system are checking different equivalences. This thesis was focused on two algorithm verifying bisimulation equivalence between two systems specific as a basic parallel processes which are available in literature. The goal was to create a verification tool that will decide bisimulation equivalence on different inputs of various sizes. This text describe how was the tool created including concepts important to the understanding of the algorithms. Correctness of the algorithms and their asymptotic complexity results from the cited sources, thesis does not include this.460 - Katedra informatikyvelmi dobř