We study versions of second-order bounded arithmetic where induction and comprehension formulae are positive or where the underlying logic is intuitionistic, examining their relationships to monotone and deep inference proof systems for propositional logic.In the positive setting a restriction of a Paris-Wilkie (PW) style translation yields quasipolynomial-size monotone propositional proofs from $Pi _1^0$ arithmetic theorems, as expected. We further show that, when only polynomial induction is used, quasipolynomialsize normal deep inference proofs may be obtained, via a graph-rewriting normalisation procedure from earlier work.For the intuitionistic setting we calibrate the PW translation with the Brouwer-Heyting-Kolmogorov interpretation of intuitionistic implication to recover a transformation to monotone proofs. By restricting type level we are able to identify an intuitionistic theory, ${I_1}U_2^1$, for which the transformation yields quasipolynomial-size monotone proofs. Conversely, we show that ${I_1}U_2^1$ is powerful enough to prove the soundness of monotone proofs, thereby establishing a full correspondence.
{"title":"From positive and intuitionistic bounded arithmetic to monotone proof complexity","authors":"Anupam Das","doi":"10.1145/2933575.2934570","DOIUrl":"https://doi.org/10.1145/2933575.2934570","url":null,"abstract":"We study versions of second-order bounded arithmetic where induction and comprehension formulae are positive or where the underlying logic is intuitionistic, examining their relationships to monotone and deep inference proof systems for propositional logic.In the positive setting a restriction of a Paris-Wilkie (PW) style translation yields quasipolynomial-size monotone propositional proofs from $Pi _1^0$ arithmetic theorems, as expected. We further show that, when only polynomial induction is used, quasipolynomialsize normal deep inference proofs may be obtained, via a graph-rewriting normalisation procedure from earlier work.For the intuitionistic setting we calibrate the PW translation with the Brouwer-Heyting-Kolmogorov interpretation of intuitionistic implication to recover a transformation to monotone proofs. By restricting type level we are able to identify an intuitionistic theory, ${I_1}U_2^1$, for which the transformation yields quasipolynomial-size monotone proofs. Conversely, we show that ${I_1}U_2^1$ is powerful enough to prove the soundness of monotone proofs, thereby establishing a full correspondence.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123689140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that the coverability problem in ν-Petri nets is complete for ‘double Ackermann’ time, thus closing an open complexity gap between an Ackermann lower bound and a hyper-Ackermann upper bound. The coverability problem captures the verification of safety properties in this nominal extension of Petri nets with name management and fresh name creation. Our completeness result establishes ν-Petri nets as a model of intermediate power among the formalisms of nets enriched with data, and relies on new algorithmic insights brought by the use of well-quasi-order ideals.Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems
{"title":"The Complexity of Coverability in ν-Petri Nets","authors":"R. Lazic, S. Schmitz","doi":"10.1145/2933575.2933593","DOIUrl":"https://doi.org/10.1145/2933575.2933593","url":null,"abstract":"We show that the coverability problem in ν-Petri nets is complete for ‘double Ackermann’ time, thus closing an open complexity gap between an Ackermann lower bound and a hyper-Ackermann upper bound. The coverability problem captures the verification of safety properties in this nominal extension of Petri nets with name management and fresh name creation. Our completeness result establishes ν-Petri nets as a model of intermediate power among the formalisms of nets enriched with data, and relies on new algorithmic insights brought by the use of well-quasi-order ideals.Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114729344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose an algebraization of classical and non-classical logics, based on factor varieties and decomposition operators. In particular, we provide a new method for determining whether a propositional formula is a tautology or a contradiction. This method can be automatized by defining a term rewriting system that enjoys confluence and strong normalization. This also suggests an original notion of logical gate and circuit, where propositional variables becomes logical gates and logical operations are implemented by substitution. Concerning formulas with quantifiers, we present a simple algorithm based on factor varieties for reducing first-order classical logic to equational logic. We achieve a completeness result for first-order classical logic without requiring any additional structure.
{"title":"Factor Varieties and Symbolic Computation","authors":"A. Salibra, Giulio Manzonetto, G. Favro","doi":"10.1145/2933575.2933600","DOIUrl":"https://doi.org/10.1145/2933575.2933600","url":null,"abstract":"We propose an algebraization of classical and non-classical logics, based on factor varieties and decomposition operators. In particular, we provide a new method for determining whether a propositional formula is a tautology or a contradiction. This method can be automatized by defining a term rewriting system that enjoys confluence and strong normalization. This also suggests an original notion of logical gate and circuit, where propositional variables becomes logical gates and logical operations are implemented by substitution. Concerning formulas with quantifiers, we present a simple algorithm based on factor varieties for reducing first-order classical logic to equational logic. We achieve a completeness result for first-order classical logic without requiring any additional structure.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133161361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andreas Krebs, Kamal Lodaya, P. Pandya, Howard Straubing
We study an extension of FO2[<], first-order logic interpreted in finite words, in which formulas are restricted to use only two variables. We adjoin to this language two-variable atomic formulas that say, ‘the letter a appears between positions x and y’. This is, in a sense, the simplest property that is not expressible using only two variables.We present several logics, both first-order and temporal, that have the same expressive power, and find matching lower and upper bounds for the complexity of satisfiability for each of these formulations. We also give an effective necessary condition, in terms of the syntactic monoid of a regular language, for a property to be expressible in this logic. We show that this condition is also sufficient for words over a two-letter alphabet. This algebraic analysis allows us us to prove, among other things, that our new logic has strictly less expressive power than full first-order logic FO[<].
{"title":"Two-variable Logic with a Between Relation","authors":"Andreas Krebs, Kamal Lodaya, P. Pandya, Howard Straubing","doi":"10.1145/2933575.2935308","DOIUrl":"https://doi.org/10.1145/2933575.2935308","url":null,"abstract":"We study an extension of FO2[<], first-order logic interpreted in finite words, in which formulas are restricted to use only two variables. We adjoin to this language two-variable atomic formulas that say, ‘the letter a appears between positions x and y’. This is, in a sense, the simplest property that is not expressible using only two variables.We present several logics, both first-order and temporal, that have the same expressive power, and find matching lower and upper bounds for the complexity of satisfiability for each of these formulations. We also give an effective necessary condition, in terms of the syntactic monoid of a regular language, for a property to be expressible in this logic. We show that this condition is also sufficient for words over a two-letter alphabet. This algebraic analysis allows us us to prove, among other things, that our new logic has strictly less expressive power than full first-order logic FO[<].","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121176168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a linear infinitary λ-calculus, called ℓΛ∞, in which two exponential modalities are available, the first one being the usual, finitary one, the other being the only construct interpreted coinductively. The obtained calculus embeds the infinitary applicative λ-calculus and is universal for computations over infinite strings. What is particularly interesting about ℓΛ∞, is that the refinement induced by linear logic allows to restrict both modalities so as to get calculi which are terminating inductively and productive coinductively. We exemplify this idea by analysing a fragment of ℓΛ built around the principles of SLL and 4LL. Interestingly, it enjoys confluence, contrarily to what happens in ordinary infinitary λ-calculi.
{"title":"Infinitary Lambda Calculi from a Linear Perspective","authors":"Ugo Dal Lago","doi":"10.1145/2933575.2934505","DOIUrl":"https://doi.org/10.1145/2933575.2934505","url":null,"abstract":"We introduce a linear infinitary λ-calculus, called ℓΛ<inf>∞</inf>, in which two exponential modalities are available, the first one being the usual, finitary one, the other being the only construct interpreted coinductively. The obtained calculus embeds the infinitary applicative λ-calculus and is universal for computations over infinite strings. What is particularly interesting about ℓΛ<inf>∞</inf>, is that the refinement induced by linear logic allows to restrict both modalities so as to get calculi which are terminating inductively and productive coinductively. We exemplify this idea by analysing a fragment of ℓΛ built around the principles of SLL and 4LL. Interestingly, it enjoys confluence, contrarily to what happens in ordinary infinitary λ-calculi.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132209379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article we study Gödel’s functional interpretation from the perspective of learning. We define the notion of a learning algorithm, and show that intuitive realizers of the functional interpretation of both induction and various comprehension schemas can be given in terms of these algorithms. In the case of arithmetical comprehension, we clarify how our learning realizers compare to those obtained traditionally using bar recursion, demonstrating that bar recursive interpretations of comprehension correspond to ‘forgetful’ learning algorithms. The main purpose of this work is to gain a deeper insight into the semantics of programs extracted using the functional interpretation. However, in doing so we also aim to better understand how it relates to other interpretations of classical logic for which the notion of learning is inbuilt, such as Hilbert’s epsilon calculus or the more recent learning-based realizability interpretations of Aschieri and Berardi.
{"title":"Gödel’s functional interpretation and the concept of learning","authors":"Thomas Powell","doi":"10.1145/2933575.2933605","DOIUrl":"https://doi.org/10.1145/2933575.2933605","url":null,"abstract":"In this article we study Gödel’s functional interpretation from the perspective of learning. We define the notion of a learning algorithm, and show that intuitive realizers of the functional interpretation of both induction and various comprehension schemas can be given in terms of these algorithms. In the case of arithmetical comprehension, we clarify how our learning realizers compare to those obtained traditionally using bar recursion, demonstrating that bar recursive interpretations of comprehension correspond to ‘forgetful’ learning algorithms. The main purpose of this work is to gain a deeper insight into the semantics of programs extracted using the functional interpretation. However, in doing so we also aim to better understand how it relates to other interpretations of classical logic for which the notion of learning is inbuilt, such as Hilbert’s epsilon calculus or the more recent learning-based realizability interpretations of Aschieri and Berardi.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129718874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We promote the theory of computational complexity on metric spaces: as natural common generalization of (i) the classical discrete setting of integers, binary strings, graphs etc. as well as of (ii) the bit-complexity theory on real numbers and functions according to Friedman, Ko (1982ff), Cook, Braverman et al.; as (iii) resource-bounded refinement of the theories of computability on, and representations of, continuous universes by Pour-El& Richards (1989) and Weihrauch (1993ff); and as (iv) computational perspective on quantitative concepts from classical Analysis: Our main results relate (i.e. upper and lower bound) Kolmogorov’s entropy of a compact metric space X polynomially to the uniform relativized complexity of approximating various families of continuous functions on X. The upper bounds are attained by carefully crafted oracles and bit-cost analyses of algorithms perusing them. They all employ the same representation (i.e. encoding, as infinite binary sequences, of the elements) of such spaces, which thus may be of own interest. The lower bounds adapt adversary arguments from unit-cost Information-Based Complexity to the bit model. They extend to, and indicate perhaps surprising limitations even of, encodings via binary string functions (rather than sequences) as introduced by Kawamura&Cook (SToC’2010, §3.4). These insights offer some guidance towards suitable notions of complexity for higher types.
我们推广度量空间上的计算复杂性理论:作为(i)整数，二进制字符串，图等的经典离散设置的自然共同推广，以及(ii)根据Friedman, Ko (1982ff)， Cook, Braverman等人的实数和函数的位复杂性理论;作为(iii)由Pour-El& Richards(1989)和Weihrauch (1993ff)对连续宇宙的可计算性和表征理论进行的资源限定细化;以及(iv)从经典分析中定量概念的计算视角:我们的主要结果将(即上界和下界)紧度量空间X的Kolmogorov熵多项式地与近似X上各种连续函数族的一致相对化复杂性联系起来。上界是通过精心制作的预言和对它们进行算法的比特成本分析而获得的。它们都使用这样的空间的相同表示(即编码，作为元素的无限二进制序列)，因此可能有自己的兴趣。下界将对手的观点从单位成本信息复杂度引入比特模型。正如Kawamura&Cook (SToC ' 2010，§3.4)所介绍的那样，它们扩展到甚至表明了通过二进制字符串函数(而不是序列)进行编码的令人惊讶的局限性。这些见解为更高级类型的复杂性概念提供了一些指导。
{"title":"Complexity Theory of (Functions on) Compact Metric Spaces","authors":"A. Kawamura, Florian Steinberg, M. Ziegler","doi":"10.1145/2933575.2935311","DOIUrl":"https://doi.org/10.1145/2933575.2935311","url":null,"abstract":"We promote the theory of computational complexity on metric spaces: as natural common generalization of (i) the classical discrete setting of integers, binary strings, graphs etc. as well as of (ii) the bit-complexity theory on real numbers and functions according to Friedman, Ko (1982ff), Cook, Braverman et al.; as (iii) resource-bounded refinement of the theories of computability on, and representations of, continuous universes by Pour-El& Richards (1989) and Weihrauch (1993ff); and as (iv) computational perspective on quantitative concepts from classical Analysis: Our main results relate (i.e. upper and lower bound) Kolmogorov’s entropy of a compact metric space X polynomially to the uniform relativized complexity of approximating various families of continuous functions on X. The upper bounds are attained by carefully crafted oracles and bit-cost analyses of algorithms perusing them. They all employ the same representation (i.e. encoding, as infinite binary sequences, of the elements) of such spaces, which thus may be of own interest. The lower bounds adapt adversary arguments from unit-cost Information-Based Complexity to the bit model. They extend to, and indicate perhaps surprising limitations even of, encodings via binary string functions (rather than sequences) as introduced by Kawamura&Cook (SToC’2010, §3.4). These insights offer some guidance towards suitable notions of complexity for higher types.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131036350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Higher inductive types (HITs) in homotopy type theory are a powerful generalization of inductive types. Not only can they have ordinary constructors to define elements, but also higher constructors to define equalities (paths). We say that a HIT H is non-recursive if its constructors do not quantify over elements or paths in H. The advantage of non-recursive HITs is that their elimination principles are easier to apply than those of general HITs.It is an open question which classes of HITs can be encoded as non-recursive HITs. One result of this paper is the construction of the propositional truncation via a sequence of approximations, yielding a representation as a non-recursive HIT. Compared to a related construction by van Doorn, ours has the advantage that the connectedness level increases in each step, yielding simplified elimination principles into n-types. As the elimination principle of our sequence has strictly lower requirements, we can then prove a similar result for van Doorn’s construction. We further derive general elimination principles of higher truncations (say, k-truncations) into n-types, generalizing a previous result by Capriotti et al. which considered the case n ≡ k + 1.
{"title":"Constructions with Non-Recursive Higher Inductive Types","authors":"Nicolai Kraus","doi":"10.1145/2933575.2933586","DOIUrl":"https://doi.org/10.1145/2933575.2933586","url":null,"abstract":"Higher inductive types (HITs) in homotopy type theory are a powerful generalization of inductive types. Not only can they have ordinary constructors to define elements, but also higher constructors to define equalities (paths). We say that a HIT H is non-recursive if its constructors do not quantify over elements or paths in H. The advantage of non-recursive HITs is that their elimination principles are easier to apply than those of general HITs.It is an open question which classes of HITs can be encoded as non-recursive HITs. One result of this paper is the construction of the propositional truncation via a sequence of approximations, yielding a representation as a non-recursive HIT. Compared to a related construction by van Doorn, ours has the advantage that the connectedness level increases in each step, yielding simplified elimination principles into n-types. As the elimination principle of our sequence has strictly lower requirements, we can then prove a similar result for van Doorn’s construction. We further derive general elimination principles of higher truncations (say, k-truncations) into n-types, generalizing a previous result by Capriotti et al. which considered the case n ≡ k + 1.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126355743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Michael Elberfeld, Marlin Frickenschmidt, Martin Grohe
Order-invariant formulas access an ordering on a structure’s universe, but the model relation is independent of the used ordering. They are frequently used for logic-based approaches in computer science. Order-invariant formulas capture unordered problems of complexity classes and they model the independence of the answer to a database query from low-level aspects of databases. we study the expressive power of order-invariant monadic second-order (MSO) and first-order (FO) logic on restricted classes of structures that admit certain forms of tree decompositions (not necessarily of bounded width).While order-invariant MSO is more expressive than MSO and, even, CMSO (MSO with modulo-counting predicates) in general, we show that order-invariant MSO and CMSO are equally expressive on graphs of bounded tree width and on planar graphs. This extends an earlier result for trees due to Courcelle. Moreover, we show that all properties definable in order-invariant FO are also definable in MSO on these classes. These results are applications of a theorem that shows how to lift up definability results for order-invariant logics from the bags of a graph’s tree decomposition to the graph itself.
{"title":"Order Invariance on Decomposable Structures","authors":"Michael Elberfeld, Marlin Frickenschmidt, Martin Grohe","doi":"10.1145/2933575.2934517","DOIUrl":"https://doi.org/10.1145/2933575.2934517","url":null,"abstract":"Order-invariant formulas access an ordering on a structure’s universe, but the model relation is independent of the used ordering. They are frequently used for logic-based approaches in computer science. Order-invariant formulas capture unordered problems of complexity classes and they model the independence of the answer to a database query from low-level aspects of databases. we study the expressive power of order-invariant monadic second-order (MSO) and first-order (FO) logic on restricted classes of structures that admit certain forms of tree decompositions (not necessarily of bounded width).While order-invariant MSO is more expressive than MSO and, even, CMSO (MSO with modulo-counting predicates) in general, we show that order-invariant MSO and CMSO are equally expressive on graphs of bounded tree width and on planar graphs. This extends an earlier result for trees due to Courcelle. Moreover, we show that all properties definable in order-invariant FO are also definable in MSO on these classes. These results are applications of a theorem that shows how to lift up definability results for order-invariant logics from the bags of a graph’s tree decomposition to the graph itself.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"2015 17","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132792764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Automata-logic connections are pillars of the theory of regular languages. Such connections are harder to obtain for transducers, but important results have been obtained recently for word-to-word transformations, showing that the three following models are equivalent: deterministic two-way transducers, monadic second-order (MSO) transducers, and deterministic one-way automata equipped with a finite number of registers. Nested words are words with a nesting structure, allowing to model unranked trees as their depth-first-search linearisations. In this paper, we consider transformations from nested words to words, allowing in particular to produce unranked trees if output words have a nesting structure. The model of visibly pushdown transducers allows to describe such transformations, and we propose a simple deterministic extension of this model with two-way moves that has the following properties: i) it is a simple computational model, that naturally has a good evaluation complexity; ii) it is expressive: it subsumes nested word-to-word MSO transducers, and the exact expressiveness of MSO transducers is recovered using a simple syntactic restriction; iii) it has good algorithmic/closure properties: the model is closed under composition with a unambiguous one-way letter-to-letter transducer which gives closure under regular look-around, and has a decidable equivalence problem.
{"title":"Two-Way Visibly Pushdown Automata and Transducers*","authors":"L. Dartois, E. Filiot, P. Reynier, J. Talbot","doi":"10.1145/2933575.2935315","DOIUrl":"https://doi.org/10.1145/2933575.2935315","url":null,"abstract":"Automata-logic connections are pillars of the theory of regular languages. Such connections are harder to obtain for transducers, but important results have been obtained recently for word-to-word transformations, showing that the three following models are equivalent: deterministic two-way transducers, monadic second-order (MSO) transducers, and deterministic one-way automata equipped with a finite number of registers. Nested words are words with a nesting structure, allowing to model unranked trees as their depth-first-search linearisations. In this paper, we consider transformations from nested words to words, allowing in particular to produce unranked trees if output words have a nesting structure. The model of visibly pushdown transducers allows to describe such transformations, and we propose a simple deterministic extension of this model with two-way moves that has the following properties: i) it is a simple computational model, that naturally has a good evaluation complexity; ii) it is expressive: it subsumes nested word-to-word MSO transducers, and the exact expressiveness of MSO transducers is recovered using a simple syntactic restriction; iii) it has good algorithmic/closure properties: the model is closed under composition with a unambiguous one-way letter-to-letter transducer which gives closure under regular look-around, and has a decidable equivalence problem.","PeriodicalId":206395,"journal":{"name":"2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116687118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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