Combining Symbolic Computer Algebra and Boolean Satisfiability for Automatic Debugging and Fixing of Complex Multipliers

Mahzoon, Alireza; Grobe, Daniel; Drechsler, Rolf

doi:10.1109/isvlsi.2018.00071

Cited by 21 publications

(4 citation statements)

References 15 publications

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“…In response to this need for a solver that combines the efficient search capabilities of SAT solvers with the mathematical knowledge available in CAS, a new kind of solving methodology was developed in 2015 by Zulkoski, Ganesh and others [63,64] and independently by Abraham [1], and has been further expanded since then by Bright et al [13,15]. This łSAT+CAS" solving methodology has been successfully applied to many diverse problems, including circuit veriőcation [42,49], automatic debugging [48], őnding circuits for matrix multiplication [33], computing directed Ramsey numbers [51], and őnding special kinds of sequences and matrices [14,16].…”

Section: The Sat+cas Paradigm For Combinatorial Mathematicsmentioning

confidence: 99%

A SAT Solver + Computer Algebra Attack on the Minimum Kochen-Specker Problem

Bright

2023

Preprint

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One of the most fundamental results in the foundations of quantum mechanics is the Kochen--Specker (KS) theorem, a `no-go' theorem which states that contextuality is an essential feature of any hidden-variable theory. The theorem hinges on the existence of a mathematical object called a KS vector system. Although the existence of a KS vector system was first established by Kochen and Specker, the problem of the minimum size of such a system has stubbornly remained open for over 50 years. In this paper, we present a new method based on a combination of a SAT solver and a computer algebra system (CAS) to address this problem. We improve the lower bound on the minimum number of vectors in a KS system from 22 to 23 and improve the efficiency of the search by a factor of over 1000 when compared to the most recent computational methods. Finding a minimum KS system would simplify experimental tests of the KS theorem and have direct applications in quantum information processing, specifically in the security of quantum cryptographic protocols based on complementarity, zero-error classical communication, and dimension witnessing.

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Section: The Sat+cas Paradigm For Combinatorial Mathematicsmentioning

confidence: 99%

A SAT Solver + Computer Algebra Attack on the Minimum Kochen-Specker Problem

Bright

2023

Preprint

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“…In response to this need for a solver that combines the efficient search capabilities of SAT solvers with the mathematical knowledge available in Computer Algebra Systems (CAS), a new kind of solving methodology was developed in 2015 by Edward Zulkoski, Vijay Ganesh, and Krzysztof Czarnecki [14] and independently by Erika Abraham [15], and has been further expanded since then by [16]. This SAT+CAS solving methodology has been successfully applied to many diverse problems, including circuit verification [17,18], automatic debugging [19], finding circuits for matrix multiplication [20], computing directed Ramsey numbers [21], and finding special kinds of sequences and matrices [22].…”

Section: The Sat+cas Paradigm For Combinatoricsmentioning

confidence: 99%

A SAT Solver + Computer Algebra Attack on the Minimum Kochen-Specker Problem

Bright

2023

Preprint

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One of the foundational results in quantum mechanics is the Kochen--Specker (KS) theorem, which states that any theory whose predictions agree with quantum mechanics must be contextual, i.e., a quantum observation cannot be understood as revealing a pre-existing value. The theorem hinges on the existence of a mathematical object called a KS vector system. While many KS vector systems are known to exist, the problem of finding the minimum KS vector system has remained stubbornly open for over 55 years, despite significant attempts by leading scientists and mathematicians. In this paper, we present a new method based on a combination of a SAT solver and a computer algebra system (CAS) to address this problem. Our approach improves the lower bound on the minimum number of vectors in a KS system from 22 to 24, and is about 35,000 times more efficient compared to the previous best computational methods. The increase in efficiency derives from the fact we are able to exploit the powerful combinatorial search-with-learning capabilities of a SAT solver together with the isomorph-free exhaustive generation methods of a CAS. The quest for the minimum KS vector system is motivated by myriad applications such as simplifying experimental tests of contextuality, zero-error classical communication, dimension witnessing, and the security of certain quantum cryptographic protocols. To the best of our knowledge, this is the first application of a novel SAT+CAS system to a problem in the realm of quantum foundations.

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“…They also propose an incremental approach to arithmetic circuit verification by column-based polynomial reduction. In addition, computer algebra methods have been applied to logic debugging [6,8,13,24] and approximations of arithmetic circuits [7,24].…”

Section: Computer Algebra Approachmentioning

confidence: 99%

Spectral approach to verifying non-linear arithmetic circuits

Yu¹,

Su²,

Yasin³

et al. 2019

Proceedings of the 24th Asia and South Pacific Design Automation Conference

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This paper presents a fast and effective computer algebraic method for analyzing and verifying non-linear integer arithmetic circuits using a novel algebraic spectral model. It introduces a concept of algebraic spectrum, a numerical form of polynomial expression; it uses the distribution of coefficients of the monomials to determine the type of arithmetic function under verification. In contrast to previous works, the proof of functional correctness is achieved by computing an algebraic spectrum combined with local rewriting of word-level polynomials. The speedup is achieved by propagating coefficients through the circuit using And-Inverter Graph (AIG) datastructure. The effectiveness of the method is demonstrated with experiments including standard and Booth multipliers, and other synthesized non-linear arithmetic circuits up to 1024 bits containing over 12 million gates.

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Combining Symbolic Computer Algebra and Boolean Satisfiability for Automatic Debugging and Fixing of Complex Multipliers

Cited by 21 publications

References 15 publications

A SAT Solver + Computer Algebra Attack on the Minimum Kochen-Specker Problem

A SAT Solver + Computer Algebra Attack on the Minimum Kochen-Specker Problem

A SAT Solver + Computer Algebra Attack on the Minimum Kochen-Specker Problem

Spectral approach to verifying non-linear arithmetic circuits

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