Visual Specifications for Modular Reasoning about Asynchronous Systems

Abstract

Abstract. We propose a framework that closely ties together visual specification and modular reasoning of asynchronous systems. The basis of the framework is a new notation, called Modular Timing Diagrams (MTD's), for specifying the universal properties about causality and timing of events in an asynchronous system. MTD's are complementary in nature to Message Sequence Charts, that are typically used to specify existential properties. Our framework includes two algorithms for formal reasoning with MTD's. The first is an efficient polynomial-time model checking algorithm. The second is an algorithm for automatically generating an assume-guarantee partitioning of an MTD, that exploits its inherent decompositional structure. We show how to use this decomposition for modular reasoning with MTD properties in conjunction with an asynchronous compositional reasoning rule. To illustrate the notation and our method, we describe a case study where we specified telephony features, such as call forwarding with MTD's, and verified these properties on an asynchronous telephony model. The compositional reasoning methods led to savings of 15%-80% in verification times, and comparable savings in space.

Towards Diagrammability and Efficiency in Event Sequence Languages

“…Amla et al's work on modular timing diagrams has much in common with this work [3]. Their work makes timing diagrams more expressive by combining them through non-diagrammatic operators for conjunction, iteration, and deterministic choice.…”

“…Mappings from formalized timing diagrams to deterministic weak automata [8] provide effectively linear symbolic verification algorithms [5]. That timing diagrams are not more widely used as event sequence languages suggests that they lack the expressiveness needed in industrial verification [3]. Their combination of utility and efficiency, however, raises an interesting question: how expressive can we make an event sequence language while retaining both diagrammability and efficiency?…”

Compositional Model Checking of Concurrent Systems

“…In recent years, various approaches to automated assumption generation for compositional reasoning have been proposed and [6] provides a survey of several major approaches. The framework presented in [2] introduces a heuristic form of the assume-guarantee modular reasoning for asynchronous systems. In the learningbased approaches, assumptions represented by deterministic finite automata are generated with the L * learning algorithm and analysis of local counter-examples [35], [1], [15], [25], [11], [7], [24], [37].…”

Temporal Modalities for Concisely Capturing Timing Diagrams

“…The timing diagrams literature contains many variations on this core notation: diagrams may support events that contain no transitions, busses, bi-directional arrows, assumption events (to represent input from the environment) [3], or combinations of timing diagrams using regular expression operators [2]. This paper considers timing diagrams with don't-care regions and partial orders between events.…”

“…To align the searches for events, we will use LTL augmented with existential quantification over atomic propositions to introduce a special symbol called end into the word to mark the end of the diagram. 2 This problem does not exist in ∀FA, since all copies of the automaton must finish in an accepting state at the same time. Thus, in some sense, the end marker is implicitly present in ∀FA.…”