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Problems in rewriting III
[chapter]

1995
*
Lecture Notes in Computer Science
*

*Related*results include the following: The existential

*fragment*

*of*the

*subterm*ordering is decidable, but its ~Us (3"V'3")

*fragment*is not [102] . ... The first-order theory

*of*encompassment (the instance-

*of*-

*subterm*

*relation*) is decidable [19] . ...

##
###
A new method for undecidability proofs of first order theories

1992
*
Journal of symbolic computation
*

The method proposed is illustrated by proving the

doi:10.1016/0747-7171(92)90016-w
fatcat:ddhabjmntfh2jg7c2l2hdyeen4
*undecidability**of*the theory*of*a*term**algebra*modulo the axioms*of*associativity and commutativity and*of*the theory*of*a partial lexicographic path ordering ... Furthermore we are interested in showing not only*undecidability**of*the whole theory*of*1, but*of*a smallest possible*fragment**of*this theory. ... ID is the*algebra**of*FDground*terms*where < is interpreted as the*subterm**relation*. The representation*of*strings has been given in Example (1) . ...##
###
The decision problem for equational bases of algebras

1976
*
Annals of Mathematical Logic
*

Eqo is the set ofequaticns

doi:10.1016/0003-4843(76)90009-7
fatcat:do2p7jauv5gkjoaysgkj3hryzi
*of*type o. if e is the equation ~o ~ ~" then e I is ~0 and er is ~. Definition 1.3; Le~ o be a similarity type and r c Eq~,. tr = ~ei: e e r }u {e,: ee r}. ... Tarski announced that a certaiv finitely based equational theory connected*with**relation**algebras*is essentially*undecidable*in [34] . ... Tarski {34] found a finitely based undecidvble equational theory*of**relation**algebras*. ...##
###
A new method for undecidability proofs of first order theories
[chapter]

1990
*
Lecture Notes in Computer Science
*

The method proposed is illustrated by proving the

doi:10.1007/3-540-53487-3_34
fatcat:prtpemxjtfhmboysjagpajngxm
*undecidability**of*the theory*of*a*term**algebra*modulo the axioms*of*associativity and commutativity and*of*the theory*of*a partial lexicographic path ordering ... Furthermore we are interested in showing not only*undecidability**of*the whole theory*of*1, but*of*a smallest possible*fragment**of*this theory. ... ID is the*algebra**of*FDground*terms*where < is interpreted as the*subterm**relation*. The representation*of*strings has been given in Example (1) . ...##
###
Relational analysis of algebraic datatypes

2005
*
Proceedings of the 10th European software engineering conference held jointly with 13th ACM SIGSOFT international symposium on Foundations of software engineering - ESEC/FSE-13
*

Such formulas arise when using the language

doi:10.1145/1081706.1081740
dblp:conf/sigsoft/KuncakJ05
fatcat:22rzdy4s2zds7jx37vypheadsi
*of*sets and*relations*to reason about structured values such as*algebraic*datatypes. ... The key idea*of*our technique is to identify a natural syntactic class*of*formulas in*relational*logic for which reasoning about infinite structures can be reduced to reasoning about finite structures. ... Indeed, [39] shows that even the satisfiability*of*formulas*with*bounded universal quantifiers is*undecidable*(although the satisfiability*of*the purely existential*fragment**with*a*subterm**relation*is ...##
###
Relational analysis of algebraic datatypes

2005
*
Software engineering notes
*

Such formulas arise when using the language

doi:10.1145/1095430.1081740
fatcat:4kfwaivyqbb6xg4ufye3su775q
*of*sets and*relations*to reason about structured values such as*algebraic*datatypes. ... The key idea*of*our technique is to identify a natural syntactic class*of*formulas in*relational*logic for which reasoning about infinite structures can be reduced to reasoning about finite structures. ... Indeed, [39] shows that even the satisfiability*of*formulas*with*bounded universal quantifiers is*undecidable*(although the satisfiability*of*the purely existential*fragment**with*a*subterm**relation*is ...##
###
Page 3634 of Mathematical Reviews Vol. , Issue 95f
[page]

1995
*
Mathematical Reviews
*

Summary: “In this paper we give a new proof

*of**undecidability*results about*term**algebras**with**subterm**relation*. ...*with**subterm**relation*. ...##
###
Coming to terms with quantified reasoning

2017
*
Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages - POPL 2017
*

The theory

doi:10.1145/3009837.3009887
fatcat:26soclwzs5gkbkc5ao2t42vg7m
*of*finite*term**algebras*provides a natural framework to describe the semantics*of*functional languages. ... However, as the theory*of*finite*term**algebras*is not finitely axiomatizable, reasoning about quantified properties over*term**algebras*is challenging. ... Moreover, one can combine T + F T*with*other theories, going even to*undecidable**fragments**of*the combined theory*of**term**algebras*and other theories. ...##
###
Coming to Terms with Quantified Reasoning
[article]

2016
*
arXiv
*
pre-print

The theory

arXiv:1611.02908v1
fatcat:gfxm4sj7prgcrdpl3ymffnhp4m
*of*finite*term**algebras*provides a natural framework to describe the semantics*of*functional languages. ... However, as the theory*of*finite*term**algebras*is not finitely axiomatizable, reasoning about quantified properties over*term**algebras*is challenging. ... Moreover, one can combine T + F T*with*other theories, going even to*undecidable**fragments**of*the combined theory*of**term**algebras*and other theories. ...##
###
A direct algorithm for type inference in the rank-2 fragment of the second-order λ-calculus

1994
*
Proceedings of the 1994 ACM conference on LISP and functional programming - LFP '94
*

We s h o w that typability is an

doi:10.1145/182409.182456
dblp:conf/lfp/KfouryW94
fatcat:b56pwql3qzgldahjpzvfdbetky
*undecidable*problem at every rank k 3*of*this strati cation. ... We study the problem*of*type inference for a family*of*polymorphic type disciplines containing the power*of*Core-ML. ... The two problems are*undecidable*for every*fragment*o f F*of*rank 3 and are decidable for rank 2. ...##
###
A direct algorithm for type inference in the rank-2 fragment of the second-order λ-calculus

1994
*
ACM SIGPLAN Lisp Pointers
*

We s h o w that typability is an

doi:10.1145/182590.182456
fatcat:k3gcffot4ba5doahsouw47blv4
*undecidable*problem at every rank k 3*of*this strati cation. ... We study the problem*of*type inference for a family*of*polymorphic type disciplines containing the power*of*Core-ML. ... The two problems are*undecidable*for every*fragment*o f F*of*rank 3 and are decidable for rank 2. ...##
###
Sort inheritance for order-sorted equational presentations
[chapter]

1995
*
Lecture Notes in Computer Science
*

We focus in this work on testing sort inheritance, an

doi:10.1007/bfb0014436
fatcat:3gatoaoiuzai7as2rvpzarelyq
*undecidable*property*of*speci cations, needed for uni cation in this context. ... In an*algebraic*framework, where equational, membership and existence formulas can be expressed, decorated*terms*and rewriting provide operational semantics and decision procedures for these formulas. ... We currently investigate*relations**with*uni ed*algebras*Mos89] or many-sorted*algebras**with*semantic sorts and sort operations Mei92]. ...##
###
More problems in rewriting
[chapter]

1993
*
Lecture Notes in Computer Science
*

Any rewrite

doi:10.1007/3-540-56868-9_39
fatcat:cibthhywyrgmvcsv73tryp3v2e
*relation*comnmtes*with*the strict-*subterm**relation*; hence, the union*of*the latter*with*an arbitrary terminating rewrite*relation*is terminating, and atso "fully htvariant" (closed under instantiation ...*with*linear constant restrictions is*undecidable*? ...##
###
Ordered fragments of first-order logic
[article]

2021
*
arXiv
*
pre-print

Using a recently introduced

arXiv:2103.08046v1
fatcat:p26sgfqkfvhbfbz7wknaf657xq
*algebraic*framework for the classification*of**fragments**of*first-order logic, we study the complexity*of*the satisfiability problem for several ordered*fragments**of*first-order ... logic, which are obtained from the ordered logic and the fluted logic by modifying some*of*their syntactical restrictions. ... The author also wishes to thank Antti Kuusisto for many helpful discussions on*fragments**of*first-order logic. ...##
###
Reachability of Hennessy-Milner Properties for Weakly Extended PRS
[chapter]

2005
*
Lecture Notes in Computer Science
*

We also strengthen some

doi:10.1007/11590156_17
fatcat:rejc2vclcveshp6idkhh67tg6y
*related**undecidability*results on some PRS subclasses. ... As a corollary we observe that the problem*of*strong bisimilarity between wPRS and finite-state systems is decidable. ... p ∈ M (∆) and each*term*t over C*with*all idle*subterms*in IdleTerms, there is a rule*of*Rules(h) applicable to p t.D. ...
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