Matches in SemOpenAlex for { <https://semopenalex.org/work/W3014070714> ?p ?o ?g. }
- W3014070714 abstract "This paper is the confluence of two streams of ideas in the literature on generating numerical invariants, namely: (1) template-based methods, and (2) recurrence-based methods. A template-based method begins with a template that contains unknown quantities, and finds invariants that match the template by extracting and solving constraints on the unknowns. A disadvantage of template-based methods is that they require fixing the set of terms that may appear in an invariant in advance. This disadvantage is particularly prominent for non-linear invariant generation, because the user must supply maximum degrees on polynomials, bases for exponents, etc. On the other hand, recurrence-based methods are able to find sophisticated non-linear mathematical relations, including polynomials, exponentials, and logarithms, because such relations arise as the solutions to recurrences. However, a disadvantage of past recurrence-based invariant-generation methods is that they are primarily loop-based analyses: they use recurrences to relate the pre-state and post-state of a loop, so it is not obvious how to apply them to a recursive procedure, especially if the procedure is non-linearly recursive (e.g., a tree-traversal algorithm). In this paper, we combine these two approaches and obtain a technique that uses templates in which the unknowns are functions rather than numbers, and the constraints on the unknowns are recurrences. The technique synthesizes invariants involving polynomials, exponentials, and logarithms, even in the presence of arbitrary control-flow, including any combination of loops, branches, and (possibly non-linear) recursion. For instance, it is able to show that (i) the time taken by merge-sort is $O(n log(n))$, and (ii) the time taken by Strassen's algorithm is $O(n^{log_2(7)})$." @default.
- W3014070714 created "2020-04-03" @default.
- W3014070714 creator A5002324370 @default.
- W3014070714 creator A5041698482 @default.
- W3014070714 creator A5066155126 @default.
- W3014070714 creator A5074534485 @default.
- W3014070714 date "2020-03-30" @default.
- W3014070714 modified "2023-09-27" @default.
- W3014070714 title "Templates and Recurrences: Better Together" @default.
- W3014070714 cites W1563374593 @default.
- W3014070714 cites W1585981132 @default.
- W3014070714 cites W1589297860 @default.
- W3014070714 cites W193346698 @default.
- W3014070714 cites W1967845657 @default.
- W3014070714 cites W1992296379 @default.
- W3014070714 cites W2003295303 @default.
- W3014070714 cites W2043100293 @default.
- W3014070714 cites W2058033966 @default.
- W3014070714 cites W2098045685 @default.
- W3014070714 cites W2111366004 @default.
- W3014070714 cites W2398327122 @default.
- W3014070714 cites W2460148525 @default.
- W3014070714 cites W2461846980 @default.
- W3014070714 cites W2522017073 @default.
- W3014070714 cites W2600895373 @default.
- W3014070714 cites W2625924363 @default.
- W3014070714 cites W2752394241 @default.
- W3014070714 cites W2797613250 @default.
- W3014070714 cites W2800657975 @default.
- W3014070714 cites W2899269697 @default.
- W3014070714 cites W2899568449 @default.
- W3014070714 cites W2963835510 @default.
- W3014070714 cites W2980978064 @default.
- W3014070714 cites W3009691493 @default.
- W3014070714 cites W3033229382 @default.
- W3014070714 cites W30585784 @default.
- W3014070714 cites W42768900 @default.
- W3014070714 cites W589969373 @default.
- W3014070714 hasPublicationYear "2020" @default.
- W3014070714 type Work @default.
- W3014070714 sameAs 3014070714 @default.
- W3014070714 citedByCount "0" @default.
- W3014070714 crossrefType "posted-content" @default.
- W3014070714 hasAuthorship W3014070714A5002324370 @default.
- W3014070714 hasAuthorship W3014070714A5041698482 @default.
- W3014070714 hasAuthorship W3014070714A5066155126 @default.
- W3014070714 hasAuthorship W3014070714A5074534485 @default.
- W3014070714 hasConcept C11413529 @default.
- W3014070714 hasConcept C114614502 @default.
- W3014070714 hasConcept C134306372 @default.
- W3014070714 hasConcept C136119220 @default.
- W3014070714 hasConcept C140745168 @default.
- W3014070714 hasConcept C168773036 @default.
- W3014070714 hasConcept C190470478 @default.
- W3014070714 hasConcept C199360897 @default.
- W3014070714 hasConcept C201292218 @default.
- W3014070714 hasConcept C202444582 @default.
- W3014070714 hasConcept C28826006 @default.
- W3014070714 hasConcept C33923547 @default.
- W3014070714 hasConcept C37914503 @default.
- W3014070714 hasConcept C39927690 @default.
- W3014070714 hasConcept C41008148 @default.
- W3014070714 hasConcept C82714645 @default.
- W3014070714 hasConceptScore W3014070714C11413529 @default.
- W3014070714 hasConceptScore W3014070714C114614502 @default.
- W3014070714 hasConceptScore W3014070714C134306372 @default.
- W3014070714 hasConceptScore W3014070714C136119220 @default.
- W3014070714 hasConceptScore W3014070714C140745168 @default.
- W3014070714 hasConceptScore W3014070714C168773036 @default.
- W3014070714 hasConceptScore W3014070714C190470478 @default.
- W3014070714 hasConceptScore W3014070714C199360897 @default.
- W3014070714 hasConceptScore W3014070714C201292218 @default.
- W3014070714 hasConceptScore W3014070714C202444582 @default.
- W3014070714 hasConceptScore W3014070714C28826006 @default.
- W3014070714 hasConceptScore W3014070714C33923547 @default.
- W3014070714 hasConceptScore W3014070714C37914503 @default.
- W3014070714 hasConceptScore W3014070714C39927690 @default.
- W3014070714 hasConceptScore W3014070714C41008148 @default.
- W3014070714 hasConceptScore W3014070714C82714645 @default.
- W3014070714 hasLocation W30140707141 @default.
- W3014070714 hasOpenAccess W3014070714 @default.
- W3014070714 hasPrimaryLocation W30140707141 @default.
- W3014070714 hasRelatedWork W1571308956 @default.
- W3014070714 hasRelatedWork W1602616602 @default.
- W3014070714 hasRelatedWork W1614799361 @default.
- W3014070714 hasRelatedWork W1983743030 @default.
- W3014070714 hasRelatedWork W1984135693 @default.
- W3014070714 hasRelatedWork W1984478102 @default.
- W3014070714 hasRelatedWork W2043228773 @default.
- W3014070714 hasRelatedWork W2075820135 @default.
- W3014070714 hasRelatedWork W2109196057 @default.
- W3014070714 hasRelatedWork W2138106543 @default.
- W3014070714 hasRelatedWork W2237322174 @default.
- W3014070714 hasRelatedWork W2570845103 @default.
- W3014070714 hasRelatedWork W2725186154 @default.
- W3014070714 hasRelatedWork W2729356611 @default.
- W3014070714 hasRelatedWork W2949823252 @default.
- W3014070714 hasRelatedWork W3033229382 @default.
- W3014070714 hasRelatedWork W3042961015 @default.
- W3014070714 hasRelatedWork W3108680707 @default.