Two decidability problems for infinite words
Information Processing Letters
Information Processing Letters
Monadic second-order definable graph transductions: a survey
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
Macro tree transducers, attribute grammars, and MSO definable tree translations
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MSO definable string transductions and two-way finite-state transducers
ACM Transactions on Computational Logic (TOCL)
Polynomial Time Algorithm for the Equivalence of two Morphisms on Omega-Regular Languages
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
Determinization of Transducers over Infinite Words: The General Case
Theory of Computing Systems
Elements of Automata Theory
Streaming transducers for algorithmic verification of single-pass list-processing programs
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Nondeterministic streaming string transducers
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
From Monadic Second-Order Definable String Transformations to Transducers
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
From Two-Way to One-Way Finite State Transducers
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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The theory of regular transformations of finite strings is quite mature with appealing properties. This class can be equivalently defined using both logic (Monadic second-order logic) and finite-state machines (two-way transducers, and more recently, streaming string transducers); is closed under operations such as sequential composition and regular choice; and problems such as functional equivalence and type checking, are decidable for this class. In this paper, we initiate a study of transformations of infinite strings. The MSO-based definition for regular string transformations generalizes naturally to infinite strings. We define an equivalent generalization of the machine model of streaming string transducers to infinite strings. A streaming string transducer is a deterministic machine that makes a single pass over the input string, and computes the output fragments using a finite set of string variables that are updated in a copyless manner at each step. We show how Muller acceptance condition for automata over infinite strings can be generalized to associate an infinite output string with an infinite execution. The proof that our model captures all MSO-definable transformations uses two-way transducers. Unlike the case of finite strings, MSO-equivalent definition of two-way transducers over infinite strings needs to make decisions based on omega-regular look-ahead. Simulating this look-ahead using multiple variables with copyless updates, is the main technical challenge in our constructions. Finally, we show that type checking and functional equivalence are decidable for MSO-definable transformations of infinite strings.