Computation tree logic CTL* and path quantifiers in the monadic theory of the binary tree
14th International Colloquium on Automata, languages and programming
Definability with bounded number of bound variables
Information and Computation
Handbook of theoretical computer science (vol. B)
Handbook of theoretical computer science (vol. B)
A propositional modal logic of time intervals
Journal of the ACM (JACM)
Embedding time granularity in a logical specification language for synchronous real-time systems
6IWSSD Selected Papers of the Sixth International Workshop on Software Specification and Design
CTL and ECTL as fragments of the modal &mgr;-calculus
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
Research perspectives for time series management systems
ACM SIGMOD Record
Reasoning about infinite computations
Information and Computation
Temporal modules: an approach toward federated temporal databases
Information Sciences—Informatics and Computer Science: An International Journal
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Logical design for temporal databases with multiple granularities
ACM Transactions on Database Systems (TODS)
Reasoning about qualitative trends in databases
Information Systems
Temporal FDs on complex objects
ACM Transactions on Database Systems (TODS)
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
An Algebraic Representation of Calendars
Annals of Mathematics and Artificial Intelligence
Discovering Frequent Event Patterns with Multiple Granularities in Time Sequences
IEEE Transactions on Knowledge and Data Engineering
Implementing Calendars and Temporal Rules in Next Generation Databases
Proceedings of the Tenth International Conference on Data Engineering
ICDE '95 Proceedings of the Eleventh International Conference on Data Engineering
Sometimes "Tomorrow" is "Sometime" - Action Refinement in a Temporal Logic of Objects
ICTL '94 Proceedings of the First International Conference on Temporal Logic
Decidability of Interval Temporal Logics over Split-Frames via Granularity
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
On-Line Model Checking for Finite Linear Temporal Logic Specifications
Proceedings of the International Workshop on Automatic Verification Methods for Finite State Systems
A Data Model for Time-Series Analysis
Advanced Database Systems
Memory Efficient Algorithms for the Verification of Temporal Properties
CAV '90 Proceedings of the 2nd International Workshop on Computer Aided Verification
The VLDB Journal — The International Journal on Very Large Data Bases
A general framework and reasoning models for time granularity
TIME '96 Proceedings of the 3rd Workshop on Temporal Representation and Reasoning (TIME'96)
Dynamic temporal interpretation contexts for temporal abstraction
TIME '96 Proceedings of the 3rd Workshop on Temporal Representation and Reasoning (TIME'96)
Representing interaction of agents at different time granularities
TIME '96 Proceedings of the 3rd Workshop on Temporal Representation and Reasoning (TIME'96)
A Logical Approach to Represent and Reason about Calendars
TIME '02 Proceedings of the Ninth International Symposium on Temporal Representation and Reasoning (TIME'02)
Reasoning about digital circuits
Reasoning about digital circuits
Dealing with different time scales in formal specifications
IWSSD '91 Proceedings of the 6th international workshop on Software specification and design
An algebraic approach to granularity in qualitative time and space representation
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Compact and tractable automaton-based representations of time granularities
Theoretical Computer Science
A modular approach to user-defined symbolic periodicities
Data & Knowledge Engineering
A timeband framework for modelling real-time systems
Real-Time Systems
Modelling temporal behaviour in complex systems with Timebands
Formal Methods in System Design
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The ability of providing and relating temporal representations at different ‘grain levels’ of the same reality is an important research theme in computer science and a major requirement for many applications, including formal specification and verification, temporal databases, data mining, problem solving, and natural language understanding. In particular, the addition of a granularity dimension to a temporal logic makes it possible to specify in a concise way reactive systems whose behaviour can be naturally modeled with respect to a (possibly infinite) set of differently-grained temporal domains. Suitable extensions of the monadic second-order theory of $k$ successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.