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Decidability of definability
[article]

2012
*
arXiv
*
pre-print

We also obtain

arXiv:1012.2381v4
fatcat:gfgrj2mcdzbbzhsrwtsq4am34m
*decidability**of*the problem when we replace primitive positive*definability*by existential positive, or existential*definability*. ... We show*decidability**of*this problem for all structures \Gamma\ that have a first-order definition in an ordered homogeneous structure \Delta\ with a finite relational signature whose age is a Ramsey class ... We will show here*decidability**of*Expr pp (Γ) for a large class*of*structures Γ which we will now*define*. Let τ be a finite relational signature. ...##
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Decidability of Definability

2013
*
Journal of Symbolic Logic (JSL)
*

We also obtain

doi:10.2178/jsl.7804020
fatcat:la3j7odll5fyrnqripall56s5q
*decidability**of*the problem when we replace primitive positive*definability*by existential positive, or existential*definability*. ... We show*decidability**of*this problem for all structures Γ that have a first-order definition in an ordered homogeneous structure Δ with a finite relational signature whose age is a Ramsey class and determined ... Theorem 1 then shows that primitive positive*definability*in fragments*of*Allen's Interval Algebra is*decidable*. ...##
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Decidability of Definability

2011
*
2011 IEEE 26th Annual Symposium on Logic in Computer Science
*

We also obtain

doi:10.1109/lics.2011.11
dblp:conf/lics/BodirskyPT11
fatcat:xob3ubxjqzd5tfaqdm7qukstze
*decidability**of*the problem when we replace primitive positive*definability*by existential positive, or existential*definability*. ... We show*decidability**of*this problem for all structures Γ that have a first-order definition in an ordered homogeneous structure ∆ with a finite relational signature whose age is a Ramsey class and determined ... Theorem 1 then shows that primitive positive*definability*in fragments*of*Allen's Interval Algebra is*decidable*. ...##
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Deciding FO-definability of regular languages
[article]

2021
*
arXiv
*
pre-print

We prove that, similarly to known PSpace-completeness

arXiv:2105.06202v5
fatcat:z6hsq4u2pbf4hkl36uo6rrueoi
*of*recognising FO(<)-*definability**of*the language L(A)*of*a DFA A,*deciding*both FO(<,C)- and FO(<,MOD)-*definability*are PSpace-complete. ... These FO-languages are known to*define*regular languages that are*decidable*in AC0 and ACC0, respectively.) ...*Deciding*L-*definability**of*2NFAs in PSpace Using the criterion Theorem 1 (i), Stern [25] showed that*deciding*whether the language*of*any given DFA is FO(<)-*definable*can be done in PSpace. ...##
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Deciding the weak definability of Büchi definable tree languages

2013
*
Annual Conference for Computer Science Logic
*

Cost automata can be used to help prove the

doi:10.4230/lipics.csl.2013.215
dblp:conf/csl/ColcombetKLB13
fatcat:yr2d3x34wrcltgdxus2ftv6yai
*decidability**of*some*definability*problems for regular languages*of*infinite trees. ... an acceptance game is just a labelling*of*the input tree with states (called a run) The weak*definability*problem is*decidable*if L(U) is deterministic. ...##
###
Decidability of definability issues in the theory of real addition
[article]

2022
*
arXiv
*
pre-print

that the corresponding theory is

arXiv:2102.06160v4
fatcat:p7pzibnjg5bmxddhdobr2x3oq4
*decidable*. ... In particular these results apply to the class*of*k-recognizable relations on reals, and allow us to prove that it is*decidable*whether a k-recognizable relation (*of*any arity) is l-recognizable for every ... More precisely we show that for every*decidable*expansion M*of*R, +, <, 1 such that every nonempty M-*definable*relation contains a point with rational components, one can*decide*whether or not a given ...##
###
First Order Decidability and Definability of Integers in Infinite Algebraic Extensions of Rational Numbers
[article]

2014
*
arXiv
*
pre-print

We also obtain a structural sufficient condition for

arXiv:1307.0743v3
fatcat:3r54m2fykff6bd73j7c3xpocga
*definability**of*the ring*of*integers over its field*of*fractions. ... We extend results*of*Videla and Fukuzaki to*define*algebraic integers in large classes*of*infinite algebraic extensions*of*Q and use these definitions for some*of*the fields to show the first-order undecidability ... Is the ring*of*integers*of*K inf first-order*definable*over K inf ? Question 1.2. Is the first-order theory*of*K inf*decidable*? ...##
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Deciding Twig-definability of Node Selecting Tree Automata

2015
*
Theory of Computing Systems
*

Since the queries

doi:10.1007/s00224-015-9623-7
fatcat:k547o5dygvagdpu5ivuehxwbwa
*definable*by NSTAs form a strict superset*of*twig-*definable*queries, we study the complexity*of*the problem to*decide*whether the query by a given NSTA is twig-*definable*. ... In addition, we show that it is also EXPTIME-complete to*decide*whether the query by a given NSTA is*definable*by a node selecting string automaton. ... First*of*all, it would be interesting to identify meaningful subclasses*of*NSTAs for which*deciding*twig-*definability*is tractable. ...##
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Deciding twig-definability of node selecting tree automata

2012
*
Proceedings of the 15th International Conference on Database Theory - ICDT '12
*

Since the queries

doi:10.1145/2274576.2274584
dblp:conf/icdt/AntonopoulosHMN12
fatcat:yhnocxbynzatlpi7mqnqmzmxmm
*definable*by NSTAs form a strict superset*of*twig-*definable*queries, we study the complexity*of*the problem to*decide*whether the query by a given NSTA is twig-*definable*. ... In addition, we show that it is also EXPTIME-complete to*decide*whether the query by a given NSTA is*definable*by a node selecting string automaton. ... First*of*all, it would be interesting to identify meaningful subclasses*of*NSTAs for which*deciding*twig-*definability*is tractable. ...##
###
Definability and decidability for rings of integers in totally imaginary fields
[article]

2022
*
arXiv
*
pre-print

We show that the ring

arXiv:2207.00140v1
fatcat:eu5bxn32end7pnyshma66pgueu
*of*integers*of*ℚ^tr is existentially*definable*in the ring*of*integers*of*ℚ^tr(i), where ℚ^tr denotes the field*of*all totally real numbers. ... This implies that the ring*of*integers*of*ℚ^tr(i) is undecidable and first-order non-*definable*in ℚ^tr(i). ... Undecidability The*definability*results in the preceding section have immediate consequences for*decid*- ability. ...##
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Characterizing and Deciding MSO-Definability of Macro Tree Transductions
[chapter]

2000
*
Lecture Notes in Computer Science
*

A macro tree transduction is MSO

doi:10.1007/3-540-46541-3_45
fatcat:64las3bm35gqldwoda3tf7abdm
*definable*if and only if it is*of*linear size increase. Furthermore, it is*decidable*for a macro tree transduction whether or not it is MSO*definable*. ... Moreover we prove that it is*decidable*whether M 's transduction is*of*linear size increase, and hence whether it is MSO*definable*. ... In cases*of**decidability*there is often a characterization*of*the subclass that is independent*of*the device that*defines*the whole class, analogous to our linear size increase characterization (as an ...##
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Definability and decidability of binary predicates for time granularity

2006
*
Journal of Applied Logic
*

In this paper we study the

doi:10.1016/j.jal.2005.06.004
fatcat:fsofugplxrd6roh2aefmmgduki
*definability*and*decidability**of*binary predicates for time granularity in monadic languages interpreted over finitely and infinitely layered structures. ... We give a number*of*positive and negative results by reduction to/from a wide spectrum*of**decidable*/undecidable problems. ... MPL P*Decidable**Decidable*? ? MCL P*Decidable**Decidable*? ? MSO = MSO P*Decidable**Decidable*Undecidable Undecidable As we have already shown, ⊕ i 1 can be*defined*in terms*of*D i . ...##
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Decidability and definability with circumscription

1987
*
Annals of Pure and Applied Logic
*

With general formula circumscription we can

doi:10.1016/0168-0072(87)90062-5
fatcat:kwayy4yrf5gcvhp5rch4yqoc4y
*define*several infinite cardinals, so the*decidability*problems are dependent upon the axioms*of*set theory. ... The set*of*structures*definable*(up to isomorphism) as first order*definable*subsets*of*countably infinite minimal models is the set*of*structures which are A2 ~ over the integers, for both forms*of*circumscription ... Also (L(to~k), e }*Decidability*and*definability*with circumscription 185 KP and (L(tro), ~) ~ KP. ...##
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Diophantine Definability and Decidability in the Extensions of Degree 2 of Totally Real Fields
[article]

2006
*
arXiv
*
pre-print

We investigate Diophantine

arXiv:math/0606368v1
fatcat:fizhcnjkvvfy5oxkjs5fi2rxj4
*definability*and*decidability*over some subrings*of*algebraic numbers contained in quadratic extensions*of*totally real algebraic extensions*of*Q. ... The*definability*and undecidability results for integral closures*of*"small" and "big" subrings*of*number fields in the infinite algebraic extensions*of*Q, previously shown by the author to hold for totally ... Given our assumptions on the degrees*of*the extensions, Gal(KE(β)/K) = Gal(K(β)/K))×Gal(E/Z). Let σ be the generator*of*Gal(K(β)/K) and let τ be a generator*of*Gal(E/Z). ...##
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MSO-definable Properties of Muller Context-Free Languages Are Decidable
[chapter]

2016
*
Lecture Notes in Computer Science
*

We show that it is

doi:10.1007/978-3-319-41114-9_7
fatcat:4dumxlmqing7zhdfn62rwzd52e
*decidable*given an MSO-*definable*property P*of*countable words and a Muller context-free grammar G, whether every word in the language generated by G satisfies P . ... As a corollary, we obtain the main result*of*this note. Theorem 1. It is*decidable*for a given MCFL L and an MSO-*definable*property ϕ*of*words whether every member*of*L satisfies ϕ. Proof. ... Also, there is an algorithm to*decide*, for a Muller tree automaton and an MSO-*definable*property*of*trees whether every tree in the language L recognized by the automaton has property P . ...
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