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30
Streaming transducers for algorithmic verification of singlepass listprocessing programs
 In 38th ACM SIGACTSIGPLAN Symposium on Princples of Programming Languages (POPL’11
, 2011
"... We introduce streaming data string transducers that map input data strings to output data strings in a single lefttoright pass in linear time. Data strings are (unbounded) sequences of data values, tagged with symbols from a finite set, over a potentially infinite data domain that supports only th ..."
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Cited by 33 (8 self)
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We introduce streaming data string transducers that map input data strings to output data strings in a single lefttoright pass in linear time. Data strings are (unbounded) sequences of data values, tagged with symbols from a finite set, over a potentially infinite data domain that supports only the operations of equality and ordering. The transducer uses a finite set of states, a finite set of variables ranging over the data domain, and a finite set of variables ranging over data strings. At every step, it can make decisions based on the next input symbol, updating its state, remembering the input data value in its data variables, and updating datastring variables by concatenating datastring variables and new symbols formed from data variables, while avoiding duplication. We establish that the problems of checking functional equivalence of two streaming transducers, and of checking whether a streaming transducer satisfies pre/post
Macro Tree Translations of Linear Size Increase are MSO Definable
 SIAM J. Comput
, 2001
"... Abstract. The first main result is that if a macro tree translation is of linear size increase, i.e., if the size of every output tree is linearly bounded by the size of the corresponding input tree, then the translation is MSO definable (i.e., definable in monadic secondorder logic). This gives a ..."
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Cited by 25 (9 self)
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Abstract. The first main result is that if a macro tree translation is of linear size increase, i.e., if the size of every output tree is linearly bounded by the size of the corresponding input tree, then the translation is MSO definable (i.e., definable in monadic secondorder logic). This gives a new characterization of the MSO definable tree translations in terms of macro tree transducers: they are exactly the macro tree translations of linear size increase. The second main result is that given a macro tree transducer, it can be decided whether or not its translation is MSO definable, and if it is then an equivalent MSO transducer can be constructed. Similar results hold for attribute grammars, which define a subclass of the macro tree translations.
Streaming tree transducers
 CoRR
"... Theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as XML documents. We introduce streaming tree transducers as an analyzable, executable, and expressiv ..."
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Cited by 11 (4 self)
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Theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as XML documents. We introduce streaming tree transducers as an analyzable, executable, and expressive model for transforming unranked ordered trees (and hedges) in a single pass. Given a linear encoding of the input tree, the transducer makes a single lefttoright pass through the input, and computes the output in linear time using a finitestate control, a visibly pushdown stack, and a finite number of variables that store output chunks that can be combined using the operations of stringconcatenation and treeinsertion. We prove that the expressiveness of the model coincides with transductions definable using monadic secondorder logic (MSO). Existing models of tree transducers either cannot implement all MSOdefinable transformations, or require regular look ahead that prohibits singlepass implementation. We show a variety of analysis problems such as typechecking and checking functional equivalence are decidable for our model. 1
Expressiveness of streaming string transducers
"... Streaming string transducers [1] define (partial) functions from input strings to output strings. A streaming string transducer makes a single pass through the input string and uses a finite set of variables that range over strings from the output alphabet. At every step, the transducer processes an ..."
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Cited by 11 (5 self)
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Streaming string transducers [1] define (partial) functions from input strings to output strings. A streaming string transducer makes a single pass through the input string and uses a finite set of variables that range over strings from the output alphabet. At every step, the transducer processes an input symbol, and updates all the variables in parallel using assignments whose righthandsides are concatenations of output symbols and variables with the restriction that a variable can be used at most once in a righthandside expression. It has been shown that streaming string transducers operating on strings over infinite data domains are of interest in algorithmic verification of listprocessing programs, as they lead to Pspace decision procedures for checking pre/post conditions and for checking semantic equivalence, for a welldefined class of heapmanipulating programs. In order to understand the theoretical expressiveness of streaming transducers, we focus on streaming transducers processing strings over finite alphabets, given the existence of a robust and wellstudied class of “regular ” transductions for this case. Such regular transductions can be defined either by twoway deterministic finitestate transducers, or using a logical MSObased characterization. Our main result is that the expressiveness of streaming string transducers coincides exactly with this class of regular transductions. 1
Query Automata for Nested Words
"... We study visibly pushdown automata (VPA) models for expressing and evaluating queries, expressed using MSO formulas, on words with a nesting structure (like XML documents). We define a query VPA model, which is a 2way deterministic VPA that can mark positions in a document, and show that it is equi ..."
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Cited by 9 (0 self)
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We study visibly pushdown automata (VPA) models for expressing and evaluating queries, expressed using MSO formulas, on words with a nesting structure (like XML documents). We define a query VPA model, which is a 2way deterministic VPA that can mark positions in a document, and show that it is equiexpressive as unary monadic queries. This surprising result parallels a classic result for queries on regular word languages. We also compare our model to query models on unranked trees. We then consider the algorithmic problem of evaluating, in one pass, the set of all positions satisfying a query in a streaming nested word. We present an algorithm that answers any fixed unary monadic query on a streaming document which uses, at any point, at most space O(d+I log n), where d is the depth of the document at that point and I is the number of potential answers to the query in the word processed thus far. This algorithm uses space close to the minimal space any streaming algorithm would need, and generalizes to answering nary queries. 1
Regular Functions, Cost Register Automata, and Generalized MinCost Problems
, 2012
"... Motivated by the successful application of the theory of regular languages to formal verification of finitestate systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can provide a foundation for analyzing quantitative properties o ..."
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Cited by 9 (6 self)
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Motivated by the successful application of the theory of regular languages to formal verification of finitestate systems, there is a renewed interest in developing a theory of analyzable functions from strings to numerical values that can provide a foundation for analyzing quantitative properties of finitestate systems. In this paper, we propose a deterministic model for associating costs with strings that is parameterized by operations of interest (such as addition, scaling, and min), a notion of regularity that provides a yardstick to measure expressiveness, and study decision problems and theoretical properties of resulting classes of cost functions. Our definition of regularity relies on the theory of stringtotree transducers, and allows associating costs with events that are conditional upon regular properties of future events. Our model of cost register automata allows computation of regular functions using multiple “writeonly ” registers whose values can be combined using the allowed set of operations. We show that classical shortestpath algorithms as well as algorithms designed for computing discounted costs, can be adopted for solving the mincost problems for the more general classes of functions specified in our model. Cost register automata with min and increment give a deterministic model that is equivalent to weighted automata, an extensively studied nondeterministic model, and this 1.1
Transducers with origin information
 In ICALP
, 2014
"... Call a stringtostring transducer regular if it can be realised by one of the following equivalent models: mso transductions, twoway deterministic automata with output, and streaming transducers with registers. This paper proposes to treat origin information as part of the semantics of a regular ..."
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Cited by 6 (0 self)
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Call a stringtostring transducer regular if it can be realised by one of the following equivalent models: mso transductions, twoway deterministic automata with output, and streaming transducers with registers. This paper proposes to treat origin information as part of the semantics of a regular stringtostring transducer. With such semantics, the model admits a machineindependent characterisation, Angluinstyle learning in polynomial time, as well as effective characterisations of natural subclasses such as oneway transducers or firstorder definable transducers. This paper is about stringtostring transducers which, in one of several equivalent definitions, can be described by deterministic twoway automata with output [AU70]. As shown in [EH01], this model is equivalent to mso definable string transducers. Another equivalent model, used in [AC10], is a deterministic oneway automaton with registers that store parts of the output1. Examples of such transducers include: duplication w 7 → ww; reversing w 7 → wR; a function
Maneth; Twoway finite state transducers with nested pebbles
 Proc. MFCS 2002, Lecture Notes in Computer Science 2420
, 2002
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Models of Tree Translation
"... This first chapter gives an introduction into the area of tree transducer theory, and describes the results presented in Chapters 2–6. The first section addresses general issues like translations, trees, and tree grammars. Section 2 is concerned with the different models of tree transducers that ar ..."
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Cited by 4 (1 self)
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This first chapter gives an introduction into the area of tree transducer theory, and describes the results presented in Chapters 2–6. The first section addresses general issues like translations, trees, and tree grammars. Section 2 is concerned with the different models of tree transducers that are considered in the thesis. It describes the typical problems that appear in tree transducer theory, and mentions important properties of the different tree transducer models. Section 3 describes the results of