The Program Inverter LRinv and Its Structure

Kawabe, Masahiko; Glück, Robert

doi:10.1007/978-3-540-30557-6_17

Cited by 21 publications

(13 citation statements)

References 11 publications

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“…Moreover, for the DCTRSs that are not confluent but innermost-confluent, we proposed the simplified completion procedure but it is not yet known whether or not the transformation in [30] is applicable. The inversion compiler LRinv, the closest one to the method in this paper, has been proposed for injective functions written in a functional language [9,7,10]. This compiler translates source programs into programs in a grammar language, and then inverts the grammar programs into inverse grammar programs.…”

Section: Discussionmentioning

confidence: 99%

“…Hence, they are not confluent but innermostconfluent. The operator du is an inverse of itself [9,10]. Thus, the TRS R du is also an inverse system of itself.…”

Section: Methodsmentioning

confidence: 99%

“…5 These 15 examples are introduced for the experiments of the inversion compiler LRinv [9,10] where LRinv succeeds in inverting all of them. Those examples are written in the scheme script Gauche.…”

Section: Methodsmentioning

confidence: 99%

“…Unfortunately, the site shown in[9] is not accessible now. The examples are also described briefly as functional programs in[10], and some of the detailed programs can be found in[10].…”

mentioning

confidence: 99%

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Completion after Program Inversion of Injective Functions

Nishida

Sakai

2009

Electronic Notes in Theoretical Computer Science

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Given a constructor term rewriting system that defines injective functions, the inversion compiler proposed by Nishida, Sakai and Sakabe generates a conditional term rewriting system that defines the inverse relations of the injective functions, and then the compiler unravels the conditional system into an unconditional term rewriting system. In general, the resulting unconditional system is not (innermost-)confluent even if the conditional system is (innermost-)confluent. In this paper, we propose a modification of the Knuth-Bendix completion procedure, which is used as a post-processor of the inversion compiler. Given a confluent and operationally terminating conditional system, the procedure takes the resulting unconditional systems as input. When the procedure halts successfully, it returns convergent systems that are computationally equivalent to the conditional systems. To adapt the modified procedure to the conditional systems that are not confluent but innermost-confluent, we propose a simplified variant of the modified procedure. We report that the implementations of the procedures succeed in generating innermost-convergent inverse systems for all the examples we tried.

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Section: Discussionmentioning

confidence: 99%

“…Hence, they are not confluent but innermostconfluent. The operator du is an inverse of itself [9,10]. Thus, the TRS R du is also an inverse system of itself.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…Unfortunately, the site shown in[9] is not accessible now. The examples are also described briefly as functional programs in[10], and some of the detailed programs can be found in[10].…”

mentioning

confidence: 99%

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Completion after Program Inversion of Injective Functions

Nishida

Sakai

2009

Electronic Notes in Theoretical Computer Science

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“…Counterexample-guided inductive synthesis [33] requires finitizing the domain (e.g., specifying a bound on loop unrollings and lengths of arrays), and we have found this is a significant burden. Other approaches that are specifically for inversion, rather than general program synthesis, are either hard to implement [8,12] or are quite restricted in the programs that can be inverted [11,24,41,11].…”

Section: Introductionmentioning

confidence: 99%

Path-based inductive synthesis for program inversion

et al. 2011

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In this paper, we investigate the problem of semi-automated inversion of imperative programs, which has the potential to make it much easier and less error prone to write programs that naturally pair as inverses, such as insert/delete operations, compressors/decompressors, and so on. Viewing inversion as a subproblem of program synthesis, we propose a novel synthesis technique called Path-based Inductive Synthesis (PINS) and apply it to inversion. PINS starts from a program P and a template T for its inverse. PINS then iteratively refines the space of template instantiations by exploring paths in the composition of P and T with symbolic execution. PINS uses an SMT solver to intelligently guide the refinement process, based on the paths explored so far. The key idea motivating this approach is the small path-bound hypothesis: that the behavior of a program can be summarized with a small, carefully chosen set of its program paths.We evaluated PINS by using it to invert 14 programs such as compressors (e.g., Lempel-Ziv-Welch), encoders (e.g., UUEncode), and arithmetic operations (e.g., vector rotation). Most of these examples are difficult or impossible to invert using prior techniques, but PINS was able to invert all of them. We also found that a semi-automated technique we developed to mine a template from the program to be inverted worked well. In our experiments, PINS takes between one second to thirty minutes to synthesize inverses. We believe this proof-of-concept implementation demonstrates the viability of the PINS approach to program synthesis.

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