Cătălin Dima

Distributed time-asynchronous automata

We show that the class of distributed time-asynchronous automata is more expressive than timed automata, has a decidable emptiness problem, is closed under union, concatenation, star, shuffle and renaming, but not under intersection. The closure results are obtained by showing that distributed time-asynchronous automata are equivalent with a subclass of shuffle regular expressions and its related class of stopwatch automata.

Balanced timed regular expressions

Several classes of regular expressions for timed languages accepted by timed automata have been suggested in the literature. In this article we introduce balanced timed regular expressions with colored parentheses which are equivalent to timed automata, and, differently from existing definitions, do not refer to clock values, and do not use additional operations such as intersection and renaming.

Revisiting Satisfiability and Model-Checking for CTLK with Synchrony and Perfect Recall

We show that CTL with knowledge modalities but without common knowledge has an undecidable satisfiability problem in the synchronous perfect recall semantics. We also present an adaptation of the classical model-checking algorithm for CTL that handles knowledge operators.

MODEL-CHECKING ALTERNATING-TIME TEMPORAL LOGIC WITH STRATEGIES BASED ON COMMON KNOWLEDGE IS UNDECIDABLE

We present a semantics for the Alternating-time Temporal Logic (ATL) with imperfect information, in which the participants in a coalition choose their strategies such that each agents choice is the same in all states that form the common knowledge for the coaltion. We show that ATL with this semantics has an undecidable model-checking problem if the semantics is also synchronous and the agents have perfect recall.

Sofic-Dyck Shifts

We define the class of sofic-Dyck shifts which extends the class of Markov-Dyck shifts introduced by Krieger and Matsumoto. The class of sofic-Dyck shifts is a particular class of shifts of sequences whose finite factors are unambiguous context-free languages. We show that it corresponds exactly to shifts of sequences whose set of factors is a visibly pushdown language. We give an expression of the zeta function of a sofic-Dyck shift which has a deterministic presentation.

Relating Paths in Transition Systems: The Fall of the Modal Mu-Calculus

We revisit Janin and Walukiewicz’s classic result on the expressive completeness of the modal mu-calculus w.r.t. MSO, when transition systems are equipped with a binary relation over paths. We obtain two natural extensions of MSO and the mu-calculus: MSOwith path relation and the jumping mu-calculus. While “bounded-memory” binary relations bring about no extra expressivity to either of the two logics, “unbounded-memory” binary relations make the bisimulation-invariant fragment of MSO with path relation more expressive than the jumping mu-calculus: the existence of winning strategies in games with imperfect-information inhabits the gap.

Static Fault-Tolerant Real-Time Scheduling with “Pseudo-topological” Orders

We give a graph-theoretical model for off-line fault-tolerant scheduling of dataflow algorithms onto multiprocessor architectures with distributed memory. Our framework allows the modeling of both processor and communication channel failures of the “fail silent” type (either transient or permanent), and failure masking is achieved by replicating operations and data communications. We show that, in general, the graph representing a fault-tolerant scheduling may have circuits; hence, the classical computation of starting and ending times of the operations and communications, based upon a topological order, is inapplicable. We thus provide a notion of “pseudo-topological order” that permits the computation of the starting and ending times even in the case of cyclic graphs. We also derive algorithms for computing the timeouts that are used for failure detection.

Removing All Silent Transitions from Timed Automata

We show that all *** -transitions can be removed from timed automata if we allow transitions to be labeled with periodic clock constraints and with periodic clock updates. This utilizes a representation of the reachability relation in timed automata in a generalization of Difference Logic with periodic constraints. We also show that periodic updates are necessary for the removal of *** -transitions.

A study on shuffle, stopwatches and independently evolving clocks

We show that stopwatch automata are equivalent with timed shuffle expressions, an extension of timed regular expressions with the shuffle operation. Since the emptiness problem is undecidable for stopwatch automata, and hence also for timed shuffle expressions, we introduce a decidable subclass of stopwatch automata called partitioned stopwatch automata. We give for this class an equivalent subclass of timed shuffle expressions and investigate closure properties by showing that partitioned stopwatch automata are closed under union, concatenation, star, shuffle and renaming, but not under intersection. We also show that partitioned stopwatch automata are equivalent with distributed time-asynchronous automata, which are asynchronous compositions of timed automata in which time may evolve independently.

A Nonarchimedian Discretization for Timed Languages

We give a discretization of behaviors of timed automata, in which timed languages are represented as sets of words containing action symbols, a clock tick symbol 1, and two delay symbols δ-negative delay and δ+ positive delay. Unlike the region construction, our discretization commutes with intersection. We show that discretizations of timed automata are, in general, context-sensitive languages over Σ ∪ {1, δ+, δ-}, and give a class of counter automata that accepts exactly the class of languages that are discretizations of timed automata, and show that its emptiness problem is decidable.