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Inductive Benchmarks for Automated Reasoning [article]

Marton Hajdu, Petra Hozzova, Laura Kovacs, Johannes Schoisswohl, Andrei Voronkov
2021
We present a large set of benchmarks for automated theorem provers that require inductive reasoning.  ...  Our benchmark set contains problems with inductive data types as well as integers. In addition to SMT-LIB encodings, we provide translations to some other less common input formats.  ...  Conclusions We describe our benchmark set for evaluating inductive capabilities of automated reasoners.  ... 
doi:10.34726/1563 fatcat:s43ft4r3zzelzh74wvktbdadne

Induction for SMT Solvers [chapter]

Andrew Reynolds, Viktor Kuncak
2015 Lecture Notes in Computer Science  
Our experiments show that the developed techniques have good performance and coverage of a range of inductive reasoning problems.  ...  Our experiments also show the impact of different representations of natural numbers and quantifier instantiation techniques on the performance of inductive reasoning.  ...  Acknowledgments We thank Ravichandhran Madhavan for an initial version of the Leon benchmarks and Cesare Tinelli for discussions about SMT-LIB semantics.  ... 
doi:10.1007/978-3-662-46081-8_5 fatcat:kd4apjhcijhb5lklpkmukazx44

Automating Induction by Reflection

Johannes Schoisswohl, Laura Kovács
2021 Electronic Proceedings in Theoretical Computer Science  
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers.  ...  The reason for that is that in first-order logic induction requires an infinite number of axioms, which is not a feasible input to a computer-aided theorem prover requiring a finite input.  ...  The most striking result is that Z3 is able to solve benchmarks that involve induction, even though it is a SMT-solver without any support for inductive reasoning.  ... 
doi:10.4204/eptcs.337.4 fatcat:csvdsf4lsndghndxgxeuxak3ba

Synthesizing Inductive Lemmas for Reasoning with First-Order Logic with Least Fixpoints [article]

Adithya Murali, Lucas Peña, Eion Blanchard, Christof Löding, P. Madhusudan
2021 arXiv   pre-print
However, automated reasoning for such logics has not seen much progress. Such logics, unlike pure FOL, do not even admit complete procedures, let alone decidable ones.  ...  In this paper, we undertake a foundational study of automatically finding proofs that use induction to reason in these logics.  ...  Our automation of FO+lfp reasoning builds over complete procedures for FO reasoning.  ... 
arXiv:2009.10207v2 fatcat:sbg75szo5rbxxkkhxvytrukjoe

Trace Logic for Inductive Loop Reasoning [article]

Pamina Georgiou and Bernhard Gleiss and Laura Kovács
2020 arXiv   pre-print
We guide and automate inductive loop reasoning in trace logic by using generic trace lemmas capturing inductive loop invariants.  ...  Our work is implemented in the RAPID framework, by extending and integrating superposition-based first-order reasoning within RAPID.  ...  We use trace lemmas as consequences of bounded induction to automated inductive loop reasoning in trace logic.  ... 
arXiv:2008.01387v2 fatcat:dsia6w7vkbgrbij5sxlytgf4z4

A List-machine Benchmark for Mechanized Metatheory

Andrew W. Appel, Xavier Leroy
2007 Electronical Notes in Theoretical Computer Science  
We propose a benchmark to compare theorem-proving systems on their ability to express proofs of compiler correctness.  ...  We propose specific criteria for evaluating the utility of mechanized metatheory systems; we have constructed solutions in both Coq and Twelf metatheory, and we draw conclusions about those two systems  ...  There are several reasons for Coq's superiority over Twelf here.  ... 
doi:10.1016/j.entcs.2007.01.020 fatcat:mh33agitavfbbdkrrrypxdcjxe

Syntax-Guided Termination Analysis [chapter]

Grigory Fedyukovich, Yueling Zhang, Aarti Gupta
2018 Lecture Notes in Computer Science  
We present new algorithms for proving program termination and non-termination using syntax-guided synthesis.  ...  Importantly, FreqTerm is competitive with state-of-the-art on a wide range of terminating and non-terminating benchmarks, and it significantly outperforms state-of-the-art on proving non-termination of  ...  The main challenge appeared to be in the size of benchmarks (up to 10000 lines of C code per loop) and reliance on an auxiliary inductive invariant.  ... 
doi:10.1007/978-3-319-96145-3_7 fatcat:ouq6ryb2vfda3c7dfuebrprvzm

Solving Constrained Horn Clauses over ADTs by Finite Model Finding [article]

Yurii Kostyukov, Dmitry Mordvinov, Grigory Fedyukovich
2021 arXiv   pre-print
Subsequently, modern methods in the automated inference of program invariants progress towards the construction of first-order definable invariants.  ...  We have implemented our approach and evaluated it against the state-of-art engines for the invariant inference in first-order logic for ADT-manipulating programs.  ...  All these benchmarks were intractable for all the solvers, except the finite model finder. For that reason, we omit the detailed statistics.  ... 
arXiv:2108.00225v2 fatcat:skd33ohnwfhkjdrfqt2f3wyczi

Software prefetching for indirect memory accesses

Sam Ainsworth, Timothy M. Jones
2017 2017 IEEE/ACM International Symposium on Code Generation and Optimization (CGO)  
Across a set of memory-bound benchmarks, our automated pass achieves average speedups of 1.3× and 1.1× for an Intel Haswell processor and an ARM Cortex-A57, both out-of-order cores, and performance improvements  ...  of 2.1× and 3.7× for the in-order ARM Cortex-A53 and Intel Xeon Phi.  ...  We then consider reasons for the wide variance in performance attainable through software prefetching across different architectures and benchmarks, showing that look-ahead distance, memory bandwidth,  ... 
doi:10.1109/cgo.2017.7863749 fatcat:b2acmimusrcs7doiwsxa5s2bmq

Automatic induction proofs of data-structures in imperative programs

Duc-Hiep Chu, Joxan Jaffar, Minh-Thai Trinh
2015 Proceedings of the 36th ACM SIGPLAN Conference on Programming Language Design and Implementation - PLDI 2015  
The main reason for this is the problem of avoiding circular reasoning. We overcome this with a novel checking condition.  ...  We consider the problem of automated reasoning about dynamically manipulated data structures.  ...  In this paper, we propose a general proof method for recursive predicates that includes reasoning by induction.  ... 
doi:10.1145/2737924.2737984 dblp:conf/pldi/ChuJT15 fatcat:xsa5w26zdvdsbpsn2qituyvflm

Automatic induction proofs of data-structures in imperative programs

Duc-Hiep Chu, Joxan Jaffar, Minh-Thai Trinh
2015 SIGPLAN notices  
The main reason for this is the problem of avoiding circular reasoning. We overcome this with a novel checking condition.  ...  We consider the problem of automated reasoning about dynamically manipulated data structures.  ...  In this paper, we propose a general proof method for recursive predicates that includes reasoning by induction.  ... 
doi:10.1145/2813885.2737984 fatcat:apu7ynjkyrc5zftccbeokf4psy

Diffy: Inductive Reasoning of Array Programs using Difference Invariants [article]

Supratik Chakraborty, Ashutosh Gupta, Divyesh Unadkat
2021 arXiv   pre-print
Our synergistic combination of inductive reasoning and finding simple difference invariants helps prove properties of programs that cannot be proved even by the winner of Arrays sub-category from SV-COMP  ...  This contrasts with classical techniques that rely on finding potentially complex loop invaraints for each loop in the program.  ...  We choose Vajra which also employs inductive reasoning for proving array programs and verify the benchmarks in its test-suite.  ... 
arXiv:2105.14748v2 fatcat:55a3dbqltrbsvjefuoilmdo4au

Sound and Automated Synthesis of Digital Stabilizing Controllers for Continuous Plants

Alessandro Abate, Iury Bessa, Dario Cattaruzza, Lucas Cordeiro, Cristina David, Pascal Kesseli, Daniel Kroening
2017 Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control - HSCC '17  
We present a new algorithm based on counter-example guided inductive synthesis that automates the design of digital controllers that are correct by construction.  ...  We have implemented our new algorithm in a tool called DSSynth, and are able to automatically generate stable controllers for a set of intricate plant models taken from the literature within minutes.  ...  Modern synthesis engines combine automated testing, genetic algorithms, and SMT-based automated reasoning [1, 11] .  ... 
doi:10.1145/3049797.3049802 dblp:conf/hybrid/AbateBCCDKK17 fatcat:aehrdgqxknhivbsphtlntyiswq

Automating Induction for Solving Horn Clauses [chapter]

Hiroshi Unno, Sho Torii, Hiroki Sakamoto
2017 Lecture Notes in Computer Science  
To automate inductive proofs, we introduce a novel proof system tailored to Horn constraint solving, and use a PDR-based Horn constraint solver as well as an SMT solver to discharge proof obligations arising  ...  We have implemented a relational verification tool for the OCaml functional language based on the proposed method and obtained promising results in preliminary experiments.  ...  We would like to thank Tachio Terauchi for useful discussions, and anonymous referees for their constructive comments. This work was partially supported by Kakenhi 16H05856 and 15H05706.  ... 
doi:10.1007/978-3-319-63390-9_30 fatcat:pgt2xnaoevcn7otiddwkcsiwnm

Invariant Synthesis for Incomplete Verification Engines [chapter]

Daniel Neider, Pranav Garg, P. Madhusudan, Shambwaditya Saha, Daejun Park
2018 Lecture Notes in Computer Science  
We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories.  ...  Moreover, we evaluate our framework in two verification settings, one in which verification engines need to handle quantified formulas and one in which verification engines have to reason about heap properties  ...  Techniques, similar to Dryad, for automated reasoning of dynamically manipulated data structure programs have also been proposed in [6, 7] .  ... 
doi:10.1007/978-3-319-89960-2_13 fatcat:saysfl3slnbn3mktsvtqk7mnlm
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