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Satisfying subtype inequalities in polynomial space
[chapter]
1997
Lecture Notes in Computer Science
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This paper studies the complexity of type inference in -calculus with subtyping. Type inference is equivalent to solving systems of subtype inequalities. ...
We consider simple types ordered structurally from an arbitrary set of base subtype assumptions. In this case, we give a PSPACE upper bound. ...
Conclusions We have designed a polynomial space algorithm to solve the problem of satis ability of subtype inequalities over simple types. ...
doi:10.1007/bfb0032747
fatcat:aiquebdcorex3ea5cpofu2vqd4
Satisfying subtype inequalities in polynomial space
2002
Theoretical Computer Science
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This paper studies the complexity of type inference in -calculus with subtyping. Infering types is equivalent to solving systems of subtype inequalities. ...
These inequalities are solved over simple types ordered structurally from an arbitrary set of base subtype assumptions. In this case, we give a new PSPACE upper bound. ...
Conclusions We have designed a polynomial space algorithm to solve the problem of satisÿability of subtype inequalities over simple types. ...
doi:10.1016/s0304-3975(00)00314-5
fatcat:mgxahpykqndmdc2l34rpgis4qq
Constraint automata and the complexity of recursive subtype entailment
[chapter]
1998
Lecture Notes in Computer Science
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A constraint set entails an inequality if every assignment of meanings (trees) to type expressions that satisfies all the constraints also satisfies the inequality. ...
In this paper we prove that nonstructural subtype entailment is PSPACEhard, both for finite trees (simple types) and infinite trees (recursive types). ...
that runs in polynomial space. The PSPACE result follows, because PSPACE = NPSPACE = coNPSPACE by Savitch's Theorem. ...
doi:10.1007/bfb0055089
fatcat:wstgss5oy5g3tnqwcl3wfb57ya
Some complexity bounds for subtype inequalities
1999
Theoretical Computer Science
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We study complexity of type reconstruction with subtypes. As proved recently, this problem is polynomially equivalent to checking satisfiability of systems of inequalities. ...
Subtype inequalities Let Q be a finite poset. The elements of Q are constant symbols of the signature which in addition contains a binary operation symbol --+. ...
Recent results of Hoang and Mitchell [IO] show that the problem of Type Reconstruction with Subtyping (TRS) is polynomial-time equivalent to the problem of Satisfiability of Subtype inequalities (SSI ...
doi:10.1016/s0304-3975(98)00134-0
fatcat:ezarzxnxung2foxljmwzhnb5n4
Scalable automatic test data generation from modeling diagrams
2007
Proceedings of the twenty-second IEEE/ACM international conference on Automated software engineering - ASE '07
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., whether we can generate appropriate test data) is solvable in polynomial time, and we produce a highly efficient (interactive speed) checker. ...
Brute-force mapping to input for constraint and SAT solvers does not scale: state-of-the-art solvers fail to find data to satisfy uniqueness and mandatory constraints in realistic time even for small examples ...
We can test the satisfiability of ORM − diagrams in polynomial time. ...
doi:10.1145/1321631.1321635
dblp:conf/kbse/SmaragdakisCS07
fatcat:fvphiemwcrf7fnwwof5uahbnia
Author index volume 277 (2002)
2002
Theoretical Computer Science
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., Satisfying subtype inequalities in polynomial space (1-2) 105-117 Hill, P.M., see R. Bagnara (1-2) 3-46 Ramalingam, G., On sparse evaluation representations (1-2) 119-147 Ryu, S., see K. ...
Ryu, A cost-effective estimation of uncaught exceptions in Standard ML programs (1-2) 185-217 Zaffanella, E., see R. Bagnara (1-2) 3-46 ...
doi:10.1016/s0304-3975(02)00125-1
fatcat:rqtgykg36bc3fcgvraoxpkhig4
Page 2049 of Mathematical Reviews Vol. , Issue 2003C
[page]
2003
Mathematical Reviews
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in polynomial space. ...
Various examples of this paper illustrate the usage of our fine-grained process types in distributed systems.”
2003c:68051 68N19 68N18
Frey, Alexandre (F-ENSMP-CMA; Paris)
Satisfying subtype inequalities ...
Editorial
2002
Theoretical Computer Science
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The third paper, Satisfying Subtype Inequalities in Polynomial Space by Alexandre Frey, considers a fundamental typing problem arising in object-oriented programming: type inference in presence of subtyping ...
It shows that this problem can be solved in polynomial space, closing an open question in this area. The paper, On Sparse Evaluation Representations by G. ...
but never handled in ML programs. ...
doi:10.1016/s0304-3975(00)00311-x
fatcat:lnzisbny3bazbomhnmtpel3pmu
Scalable satisfiability checking and test data generation from modeling diagrams
2008
Automated Software Engineering : An International Journal
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., whether we can generate appropriate test data) is solvable in polynomial time, and we produce a highly efficient (interactive speed) checker. ...
Brute-force mapping to input for constraint and SAT solvers does not scale: state-of-the-art solvers fail to find data to satisfy uniqueness and mandatory constraints in realistic time even for small examples ...
Furthermore, solving the inequalities can be done in polynomial time. ...
doi:10.1007/s10515-008-0044-6
fatcat:4yfmlmoxwnazpkzmmrb7nncaeq
Page 1433 of Mathematical Reviews Vol. , Issue 2000b
[page]
2000
Mathematical Reviews
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Introduction: “This article discusses various aspects of a single de- cision problem: satisfiability of subtype inequalities (abbreviated SSI). ...
Euclidean space. ...
Exponential Automatic Amortized Resource Analysis
[chapter]
2020
Lecture Notes in Computer Science
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Existing work on AARA has focused on bounds that are polynomial in the sizes of the inputs. ...
A key idea is the use of the Stirling numbers of the second kind as the basis of potential functions, which play the same role as the binomial coefficients in polynomial AARA. ...
In such a case, one finds p ≤ q, p ≥ q , and Φ(v : B) = Φ(V : Γ ). This and the non-negativity of potential are sufficient to satisfy the desired inequalities. ...
doi:10.1007/978-3-030-45231-5_19
fatcat:uwvfvwnpljh4dcxryxmgk6xaa4
Exponential Automatic Amortized Resource Analysis
[article]
2020
arXiv
pre-print
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Other Versions
Existing work on AARA has focused on bounds that are polynomial in the sizes of the inputs. ...
A key idea is the use of the Stirling numbers of the second kind as the basis of potential functions, which play the same role as the binomial coefficients in polynomial AARA. ...
This identity and the non-negativity of potential satisfy the desired inequalities. ...
arXiv:2002.09519v2
fatcat:7laqjuk3bzcf5kibtmc65dy3lm
Algorithmic aspects of type inference with subtypes
1992
Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '92
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The
"untypability"
algorithm
described
above operates
in polynomial
space, since the prepro-
cessing phases building
the DAG
may be completed
in linear
time
and space,
and the nondeterministic ...
(z2):cf-+u That
is,~must
match
/3 -
n, and thus no sub-
stitution
of types for type variables
can satisfy
those
inequations. ...
doi:10.1145/143165.143227
dblp:conf/popl/LincolnM92
fatcat:4ggkk6ij7nbnbnvyn74fofllii
Page 7109 of Mathematical Reviews Vol. , Issue 97K
[page]
1997
Mathematical Reviews
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As proved recently, this problem is polynomially equivalent to checking satisfiability of systems of inequalities. ...
inequalities. ...
Automated Real Proving in PVS via MetiTarski
[chapter]
2014
Lecture Notes in Computer Science
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The strategy bernstein automatically discharges simply-quantified multivariate polynomial inequalities. ...
In particular, the numerical types are defined such that nat (natural numbers) is a subtype of int (integers), int is a subtype of rat (rationals), rat is a subtype of real (reals), and real is a subtype ...
doi:10.1007/978-3-319-06410-9_14
fatcat:tw2yfzonk5cgjmjaoy3idzaefu
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