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### Two-Way Finite State Transducers with Nested Pebbles [chapter]

Joost Engelfriet, Sebastian Maneth
2002 Lecture Notes in Computer Science
Two-way finite state transducers are considered with a fixed number of pebbles, of which the life times are nested.  ...  The ranges of the k-pebble transducers form a hierarchy with respect to k, their finiteness problem is decidable, and they can be generated by compositions of k macro tree transducers.  ...  Acknowledgement We are grateful to Frank Neven for drawing our attention to the relation between automata theory and query languages, and in particular to the pebble tree transducer model of [20, 28]  ...

### Two-way pebble transducers for partial functions and their composition

Joost Engelfriet
2015 Acta Informatica
Two-way finite state transducers are considered that use a finite number of pebbles, of which the life times must be nested.  ...  The composition of two deterministic transducers can be realized by one such transducer with a minimal number of pebbles. 1 The mistake in the proof is explained in New Observation 5.10 of [10] .  ...  Pebble transducers A two-way finite state transducer (also called two-way generalized sequential machine, or 2gsm) is a finite state automaton with a two-way input tape, delimited by the endmarkers and  ...

### Pebble Minimization of Polyregular Functions

Nathan Lhote
2020 Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science
Moreover a polyregular function can be realized by: a transducer with two pebbles if and only if its output has quadratic size in its input, a transducer with three pebbles if and only if its output has  ...  Moreover the characterization is decidable and, given a polyregular function, one can compute a transducer realizing it with the minimal number of pebbles.  ...  A 1-pebble transducer is a tuple (Σ, Γ, Q, q I , q F , δ ), which consists of: • a finite input alphabet Σ and a finite output alphabet Γ; • a finite set of states Q; • two designated states q I and q  ...

### Transducers of polynomial growth

Mikolaj Bojanczyk
2022 Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science
The polyregular functions are a class of string-to-string functions that have polynomial size outputs, and which can be defined using finite state models.  ...  There are many equivalent definitions of this class, with roots in automata theory, programming languages and logic. This paper surveys recent results on polyregular functions.  ...  One direction is clear: a for-transducer can easily be simulated by a pebble transducer, with one pebble for each nested for loop, and with the state used to store the values of the Boolean variables and  ...

### XML transformation by tree-walking transducers with invisible pebbles

Joost Engelfriet, Hendrik Jan Hoogeboom, Bart Samwel
2007 Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '07
The pebble tree automaton and the pebble tree transducer are enhanced by additionally allowing an unbounded number of 'invisible' pebbles (as opposed to the usual 'visible' ones).  ...  The resulting pebble tree transducers can apply arbitrary MSO definable tests to (the observable part of) their configurations, they (still) have a decidable typechecking problem, and they can model the  ...  Thus, the life times of the pebbles on the tree are nested. Here we consider two types of pebbles. First there are a finite number of 'classical' pebbles, which we here call visible.  ...

### Polyregular Functions [article]

Mikołaj Bojańczyk
2018 arXiv   pre-print
The class has four equivalent definitions: 1. deterministic two-way transducers with pebbles; 2 the smallest class of string-to-string functions that is closed under composition, contains all sequential  ...  The class of polyregular functions contains known classes of string-to-string transducers, such as the sequential, rational, or regular ones, but goes beyond them because of super-linear growth.  ...  using a two-way automaton with output.  ...

### Hiding pebbles when the output alphabet is unary [article]

Gaëtan Douéneau-Tabot
2022 arXiv   pre-print
Pebble transducers are nested two-way transducers which can drop marks (named "pebbles") on their input word.  ...  Blind transducers have been introduced by Nguy\^en et al. as a subclass of pebble transducers, which can nest two-way transducers but cannot drop pebbles on their input.  ...  Blind and pebble transducers. Blind and pebble transducers extend two-way transducers by allowing to "nest" such machines. A 1-blind (resp. 1-pebble) transducer is just a two-way transducer.  ...

### Register Transducers Are Marble Transducers

Gaëtan Douéneau-Tabot, Emmanuel Filiot, Paul Gastin, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science
Deterministic two-way transducers define the class of regular functions from words to words.  ...  In this paper, we drop the "copyless" restriction on these machines and show that they are equivalent to two-way transducers enhanced with the ability to drop marks, named "marbles", on the input.  ...  The particular model of two-way transducer consists in a two-way automaton enhanced with an output function.  ...

### XML navigation and transformation by tree-walking automata and transducers with visible and invisible pebbles

Joost Engelfriet, Hendrik Jan Hoogeboom, Bart Samwel
2020 Theoretical Computer Science
The pebble tree automaton and the pebble tree transducer are enhanced by additionally allowing an unbounded number of "invisible" pebbles (as opposed to the usual "visible" ones).  ...  The resulting pebble tree transducers can apply arbitrary MSO definable tests to (the observable part of) their configurations, they (still) have a decidable typechecking problem, and they can model the  ...  The pebble tree transducer is a tree-walking tree transducer with nested pebbles, i.e., it walks on the input tree, dropping and lifting a bounded number of pebbles that have nested life times, whereas  ...

### XML Navigation and Transformation by Tree-Walking Automata and Transducers with Visible and Invisible Pebbles [article]

Joost Engelfriet, Hendrik Jan Hoogeboom, Bart Samwel
2018 arXiv   pre-print
The pebble tree automaton and the pebble tree transducer are enhanced by additionally allowing an unbounded number of "invisible" pebbles (as opposed to the usual "visible" ones).  ...  The resulting pebble tree transducers can apply arbitrary MSO definable tests to (the observable part of) their configurations, they (still) have a decidable typechecking problem, and they can model the  ...  The pebble tree transducer is a tree-walking tree transducer with nested pebbles, i.e., it walks on the input tree, dropping and lifting a bounded number of pebbles that have nested life times, whereas  ...

### A comparison of pebble tree transducers with macro tree transducers

Joost Engelfriet, Sebastian Maneth
2003 Acta Informatica
Next, the pebble tree transducer is compared with the macro tree transducer, a well-known model for syntax-directed semantics, with decidable type checking.  ...  Finally, (4) the output languages of deterministic n-pebble tree transducers form a hierarchy with respect to the number n of pebbles.  ...  Acknowledgment We are grateful to Frank Neven for drawing our attention to the pebble tree transducer model of [MSV00, Via01] , and for asking us about its relationship to the macro tree transducer.  ...

### Register transducers are marble transducers [article]

Gaëtan Douéneau-Tabot and Emmanuel Filiot and Paul Gastin
2020 arXiv   pre-print
Deterministic two-way transducers define the class of regular functions from words to words.  ...  In this paper, we drop the "copyless" restriction on these machines and show that they are equivalent to two-way transducers enhanced with the ability to drop marks, named "marbles", on the input.  ...  Remark. 0-marble transducers are exactly two-way transducers. As special instances of 1-marble transducers we get programs with 2 nested for loops of shape for i in {1,...,|w|} ( for j in {1,...  ...

### Comparison-free polyregular functions [article]

Lê Thành Dũng Nguyên, Camille Noûs, Pierre Pradic
2021 arXiv   pre-print
" operation; a restricted variant of pebble transducers; a λ-calculus with a linear type system.  ...  Finally, we look at the recently introduced layered streaming string transducers (SSTs), or equivalently k-marble transducers.  ...  This amounts to restricting in two ways 4 the definition of pebble transducers from [4, §2]: in a general pebble transducer, one can compare positions, i.e. given a stack (i 1 , . . . , i p ), the choice  ...

### Automata for XML—A survey

Thomas Schwentick
2007 Journal of computer and system sciences (Print)
Acknowledgments The author warmly thanks Joost Engelfriet, Christoph Koch, Sebastian Maneth, Wim Martens, Maarten Marx, Frank Neven, and Volker Weber and two anonymous for very many valuable suggestions  ...  Then a two-way string automaton with output is used to compute a new state assignment for these nodes.  ...  Deterministic two-way automata with selecting states and the ability to apply the latter kind of transitions at most once per node are exactly as expressive as selecting tree automata.  ...

### Typechecking for XML transformers

Tova Milo, Dan Suciu, Victor Vianu
2000 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '00
The main result of the paper is that typechecking for k-pebble transducers is decidable.  ...  We model XML transformers using a novel device called a k-pebble transducer, that can express most queries without data-value joins in XML-QL, XSLT, and other XML query languages.  ...  Thanks also to Thomas Schwentick for pointing out the connection between k-pebble automata and star-free generalized regular expressions, yielding the lower bound in Theorem 4.8.  ...
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