An Automaton over Data Words That Captures EMSO Logic

Abstract

Abstract. We develop a general framework for the specification and implementation of systems whose executions are words, or partial orders, over an infinite alphabet. As a model of an implementation, we introduce class register automata, a one-way automata model over words with multiple data values. Our model combines register automata and class memory automata. It has natural interpretations. In particular, it captures communicating automata with an unbounded number of processes, whose semantics can be described as a set of (dynamic) message sequence charts. On the specification side, we provide a local existential monadic second-order logic that does not impose any restriction on the number of variables. We study the realizability problem and show that every formula from that logic can be effectively, and in elementary time, translated into an equivalent class register automaton.

Model Checking Languages of Data Words

“…The election phase is performed by transitions lep 4 to lep 6 . Here, the register stores the current leader which is sent to the next process in lep 4 with action e (d + 1, d, ). Moreover, A(d, d + 1) is written onto the second stack to prepare the announcement phase.…”

“…Data trees may serve as a model of XML documents where the data part refers to attribute values or text contents [3]. Data words, on the other hand, are suitable to model the behavior of concurrent programs where an unbounded number of processes communicate via message passing [4,5].…”

“…Moreover, none of them is suited to represent distributed protocols: they either run on one-dimensional data words, process a data word in several passes, or do not support concurrency. An automaton model that captures the interplay of communicating processes is due to [4]. Its modeling power, however, comes at the price of an undecidable emptiness problem.…”

A Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours

“…Related work. Automata over infinite data words have been introduced to prove decidability of satisfiability for many kinds of logic: LTL with freeze quantifier [31]; safety fragment of LTL [32]; F O with two variables, successor, and equality and order predicates [33]; EMSO with two variables, successor and equality [34]; generic EMSO [35]; EMSO with two variables and LTL with additional operators for data words [36]. The main result for these papers is decidability of nonemptiness.…”

Reasoning about Data Repetitions with Counter Systems

“…[BDM + 11, BL10,KST12]. Moreover, interesting and surprising results have been exhibited about relationships between logics for data words and counter automata (including vector addition systems with states) [BDM + 11, DL09, BL10], leading to a first classification of automata on data words [BL10,Bol11]. This is why logics for data words are not only interesting for their own sake but also for their deep relationships with data automata or with counter automata.…”