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Decidable Inequalities over Infinite Trees

unpublished

Linear

doi:10.29007/s21n
fatcat:s2dherdna5aarmiygl7y3ynurm
*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.) ...##
###
Type reconstruction with recursive types and atomic subtyping
[chapter]

1993
*
Lecture Notes in Computer Science
*

This problem reduces to the problem of solving a finite set of

doi:10.1007/3-540-56610-4_98
fatcat:ohkega6jgrabnjmw3bddjrez7q
*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*. ...##
###
Constraint automata and the complexity of recursive subtype entailment
[chapter]

1998
*
Lecture Notes in Computer Science
*

Constraints are formal

doi:10.1007/bfb0055089
fatcat:wstgss5oy5g3tnqwcl3wfb57ya
*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. ...##
###
An Automata-Theoretic Approach to Reasoning about Parameterized Systems and Specifications
[chapter]

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. ...

##
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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]

1991
*
Lecture Notes in Computer Science
*

A general result about systems of

doi:10.1007/3-540-53982-4_24
fatcat:cq5jea4k4jhdhjvp6ov3keze6u
*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. ...##
###
Type Inference with Inequalities

1990
*
DAIMI Report Series
*

A general result about systems of

doi:10.7146/dpb.v19i336.6566
fatcat:enqhb3lyznaclpqiwqiylfc6r4
*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. ...##
###
Some Perspectives of Infinite-State Verification
[chapter]

2005
*
Lecture Notes in Computer Science
*

We report on recent progress in the study of

doi:10.1007/11562948_3
fatcat:z6i5hzxbvndrvj3rq52gqym5ju
*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*...##
###
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]

2020
*
arXiv
*
pre-print

Supporting non-dense domains for features that range

arXiv:2006.02078v1
fatcat:qtuf7wqrhvbojmzlfvmh52cdim
*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 ...##
###
Almost Sure Productivity
[article]

2018
*
arXiv
*
pre-print

Intuitively, a probabilistic coinductive stream or

arXiv:1802.06283v2
fatcat:74hnlnccdbfn5hm27nfr2scfxe
*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*. ...##
###
Three Easy Pieces on Schema Mappings for Tree-structured Data

2017
*
Alberto Mendelzon Workshop on Foundations of Data Management
*

For

dblp:conf/amw/DavidM17
fatcat:vrule5zumfb3hpgyioztx7s5tm
*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*. ...##
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Deciding Regularity of the Set of Instances of a Set of Terms with Regular Constraints is EXPTIME-Complete
[article]

2009
*
arXiv
*
pre-print

The main contribution is a new, exponential time algorithm that performs various exponential transformations on the involved terms and

arXiv:0911.3674v1
fatcat:67uwtreloran5cng7vvp3ulb3u
*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. ...##
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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

2016
*
Electronic Proceedings in Theoretical Computer Science
*

Our main result is that the problem of determining if a subzero automaton accepts some regular

doi:10.4204/eptcs.223.1
fatcat:wecnbpznjrdm7c2lj4tiqi5tpe
*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 . ...
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