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Decidable Inequalities over Infinite Trees

Sabine Bauer, Steffen Jost, Martin Hofmann
unpublished
Linear tree constraints are given by pointwise linear inequalities between infinite trees labeled with nonnegative rational numbers.  ...  So far, only the case of degenerated tree constraints (i.e. lists) was known to be decidable which, however, is insufficient to generally solve the given resource analysis problem.  ...  Each inequality over tree variables corresponds to infinitely many inequalities over arithmetic variables (i.e. variables for the numbers in the nodes.)  ... 
doi:10.29007/s21n fatcat:s2dherdna5aarmiygl7y3ynurm

Type reconstruction with recursive types and atomic subtyping [chapter]

Jerzy Tiuryn, Mitchell Wand
1993 Lecture Notes in Computer Science  
This problem reduces to the problem of solving a finite set of inequalities over infinite trees.  ...  We show how to solve such inequalities by reduction to an infinite but well-structured set of inequalities over the base types. This infinite set of inequalities is solved using Biichi automata.  ...  Instead of solving inequalities over finite trees, we will need to solve inequalities over possibly infinite trees.  ... 
doi:10.1007/3-540-56610-4_98 fatcat:ohkega6jgrabnjmw3bddjrez7q

Constraint automata and the complexity of recursive subtype entailment [chapter]

Fritz Henglein, Jakob Rehof
1998 Lecture Notes in Computer Science  
Constraints are formal inequalities between type expressions, interpreted over an ordered set of possibly infinite labeled trees.  ...  For the structural ordering we prove that subtype entailment over infinite trees is PSPACE-complete, when the order on trees is generated from a lattice of type constants.  ...  This amounts to saying that, in order to decide structural subtype entailment --over finite or infinite trees --it is sufficient to consider entailment restricted to C-shaped valuations.  ... 
doi:10.1007/bfb0055089 fatcat:wstgss5oy5g3tnqwcl3wfb57ya

An Automata-Theoretic Approach to Reasoning about Parameterized Systems and Specifications [chapter]

Orna Grumberg, Orna Kupferman, Sarai Sheinvald
2013 Lecture Notes in Computer Science  
over infinite domains.  ...  We introduce generalized register automata (GRAs) and study their properties and applications in reasoning about systems and specifications over infinite domains.  ...  The system S also includes an inequality set E over X.  ... 
doi:10.1007/978-3-319-02444-8_28 fatcat:2ge5kkx4kbfsxls442ekuuanqq

Page 3550 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
Chapters 5 and 6 together give a proof of Rabin’s theorem, that the monadic second-order theory of the infinite binary tree (or of two successors, $2S) is decidable.  ...  In this context the introductory material on linear orders, trees, and the notion of decidability is especially valuable.  ... 

Type inference with inequalities [chapter]

Michael I. Schwartzbach
1991 Lecture Notes in Computer Science  
A general result about systems of inequalities over semilattices yields a solvable form.  ...  Type correctness is expressed as satisfiability of a possibly infinite collection of (monotonic) inequalities on the types of variables and expressions.  ...  The constraints are inequalities over types; they are solved using finite state automata to yield a minimal typing.  ... 
doi:10.1007/3-540-53982-4_24 fatcat:cq5jea4k4jhdhjvp6ov3keze6u

Type Inference with Inequalities

Michael I. Schwartzbach
1990 DAIMI Report Series  
A general result about systems of inequalities over semilattices yields a solvable form.  ...  Type correctness is expressed as satisfiability of a possibly infinite collection of (monotonic) inequalities on the types of variables and expressions.  ...  The constraints are inequalities over types; they are solved using finite state automata to yield a minimal typing.  ... 
doi:10.7146/dpb.v19i336.6566 fatcat:enqhb3lyznaclpqiwqiylfc6r4

Some Perspectives of Infinite-State Verification [chapter]

Wolfgang Thomas
2005 Lecture Notes in Computer Science  
We report on recent progress in the study of infinite transition systems for which interesting properties (like reachability of designated states) can be checked algorithmically.  ...  of such models are discussed: the construction from simpler models via operations like unfolding and synchronized product, and the internal representation of state spaces by regular sets of words or trees  ...  There is, of course, a different approach for infinite-state model-checking, based on the admission of infinite data structures (like counters over the natural numbers, or addition and inequalities over  ... 
doi:10.1007/11562948_3 fatcat:z6i5hzxbvndrvj3rq52gqym5ju

Page 8087 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
Summary: “We prove that it is decidable whether or not a regular language can be written as the set of all finite factors of an infinite word.  ...  Summary (translated from the Russian): “We consider global over- monoids of free monoids with an infinite number of generators. In the overmonoids we study special equality problems.  ... 

An ExpTime Upper Bound for ALC with Integers (Extended Version) [article]

Nadia Labai, Magdalena Ortiz, Mantas Šimkus
2020 arXiv   pre-print
Supporting non-dense domains for features that range over integers or natural numbers remained largely open, despite often being singled out as a highly desirable extension.  ...  For expressive DLs and in the presence of general TBoxes, for standard reasoning tasks like consistency, the most general decidability results are for the so-called ω-admissible domains, which are required  ...  In order to decide the existence of a solution over N ⇤ to an enriched system of linear inequalities (V, E, I) we can construct a set of (ordinary) linear inequality systems and check whether at least  ... 
arXiv:2006.02078v1 fatcat:qtuf7wqrhvbojmzlfvmh52cdim

Almost Sure Productivity [article]

Alejandro Aguirre, Gilles Barthe, Justin Hsu, Alexandra Silva
2018 arXiv   pre-print
Intuitively, a probabilistic coinductive stream or tree is ASP if it produces infinitely many outputs with probability 1.  ...  The reduction shows that ASP is decidable for our core language.  ...  Defining Almost Sure Productivity We will consider programs that denote probability distributions over coinductive types, such as infinite streams or trees.  ... 
arXiv:1802.06283v2 fatcat:74hnlnccdbfn5hm27nfr2scfxe

Three Easy Pieces on Schema Mappings for Tree-structured Data

Claire David, Filip Murlak
2017 Alberto Mendelzon Workshop on Foundations of Data Management  
For tree-structured data, the interplay between these specifications and the complex structural conditions imposed by the schemas, makes schema mappings a very rich formalism.  ...  Recent results on non-mixing integrity constraints help to push the decidability frontier further for three such problems: consistency of mappings, membership in the composition of mappings, and query  ...  In [1] it is shown that as soon as one forbids inequality in queries, the problem becomes decidable.  ... 
dblp:conf/amw/DavidM17 fatcat:vrule5zumfb3hpgyioztx7s5tm

Deciding Regularity of the Set of Instances of a Set of Terms with Regular Constraints is EXPTIME-Complete [article]

Omer Giménez, Guillem Godoy, Sebastian Maneth
2009 arXiv   pre-print
The main contribution is a new, exponential time algorithm that performs various exponential transformations on the involved terms and tree automata, and decides regularity by analyzing formulas over inequality  ...  Finite-state tree automata are a well studied formalism for representing term languages.  ...  . , s k are, and, of course, how expensive it is to decide the infinite instances property.  ... 
arXiv:0911.3674v1 fatcat:67uwtreloran5cng7vvp3ulb3u

Page 2820 of Mathematical Reviews Vol. , Issue 92e [page]

1992 Mathematical Reviews  
A general result about systems of inequalities over semilattices yields a solvable form.  ...  Type correctness is expressed as satis- fiability of a possibly infinite collection of (monotonic) inequalities on the types of variables and expressions.  ... 

On the Regular Emptiness Problem of Subzero Automata

Henryk Michalewski, Matteo Mio, Mikołaj Bojańczyk
2016 Electronic Proceedings in Theoretical Computer Science  
Our main result is that the problem of determining if a subzero automaton accepts some regular tree is decidable.  ...  Subzero automata is a class of tree automata whose acceptance condition can express probabilistic constraints.  ...  We assume some familiarity with tree automata over infinite trees as in, e.g., [6] . The first part of the definition matches that of ordinary nondeterministic parity tree automata 2 .  ... 
doi:10.4204/eptcs.223.1 fatcat:wecnbpznjrdm7c2lj4tiqi5tpe
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