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Satisfying subtype inequalities in polynomial space [chapter]

Alexandre Frey
1997 Lecture Notes in Computer Science  
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

Alexandre Frey
2002 Theoretical Computer Science  
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]

Fritz Henglein, Jakob Rehof
1998 Lecture Notes in Computer Science  
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

Marcin Benke
1999 Theoretical Computer Science  
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

Yannis Smaragdakis, Christoph Csallner, Ranjith Subramanian
2007 Proceedings of the twenty-second IEEE/ACM international conference on Automated software engineering - ASE '07  
., 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  
., 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  
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

Pascal Van Hentenryck
2002 Theoretical Computer Science  
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

Yannis Smaragdakis, Christoph Csallner, Ranjith Subramanian
2008 Automated Software Engineering : An International Journal  
., 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  
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]

David M. Kahn, Jan Hoffmann
2020 Lecture Notes in Computer Science  
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]

David M Kahn, Jan Hoffmann
2020 arXiv   pre-print
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

Patrick Lincoln, John C. Mitchell
1992 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '92  
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  
As proved recently, this problem is polynomially equivalent to checking satisfiability of systems of inequalities.  ...  inequalities.  ... 

Automated Real Proving in PVS via MetiTarski [chapter]

William Denman, César Muñoz
2014 Lecture Notes in Computer Science  
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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