A Grover-Meets-Simon Approach to Match Vector Boolean Functions

The Boolean matching problem via NP-equivalence requires determining whether two Boolean functions are equivalent or not up to a permutation and negation of the input binary variables. Its solution is a fundamental step in the electronic design automation (EDA) tool chains commonly used for digital...

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Vydáno v:IEEE transactions on quantum engineering Ročník 6; s. 1 - 14
Hlavní autoři: Venere, Marco, Barenghi, Alessandro, Pelosi, Gerardo
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Benchmark testing
Boolean
Boolean functions
Circuit design
Codes
Digital circuits
Digital electronics
Electronic design automation
Electronic design automation (EDA)
Equivalence
Integrated circuit interconnections
Libraries
Logic gates
Matching
negation–permutation–negation equivalence (NPN-equivalence)
Permutations
Polynomials
Quantum algorithm
quantum-aided Boolean matching
Time complexity
Vectors
ISSN:2689-1808, 2689-1808
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Shrnutí:The Boolean matching problem via NP-equivalence requires determining whether two Boolean functions are equivalent or not up to a permutation and negation of the input binary variables. Its solution is a fundamental step in the electronic design automation (EDA) tool chains commonly used for digital circuit design. In fact, the library-mapping step of an EDA workflow requires matching parts of the gate-level design ( netlist ) with the components available in a technology library, considering them as Boolean functions, while taking into account that permutations and negations of input variables can be efficiently implemented through rewiring and the use of inverters. For <inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula>-to-<inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula> vector Boolean functions, where <inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula> is the number of input and output variables, the search space of possible negations and permutations is super-exponential in size, while the <inline-formula><tex-math notation="LaTeX">\mathcal {O}(n!n2^{2n})</tex-math></inline-formula> time complexity of classical approaches allows solving only small instances of the NP-problem, often limited to <inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula>-to-1 Boolean functions (executing <inline-formula><tex-math notation="LaTeX">\mathcal {O}(n!2^{2n})</tex-math></inline-formula> bit operations). This work presents a quantum algorithm for matching <inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula>-to-<inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula> vector Boolean functions by effectively combining the Grover-meets-Simon approach with an original and novel use of the Simon solver without the constraints imposed by its usual premises. We provide a fully detailed quantum circuit implementing our proposal, calculate its cost by evaluating key performance indicators for circuit synthesis, and show an exponential speedup over classical solutions. Finally, we validate our approach on the Boolean functions included in the ISCAS benchmark suite, which are of practical interest in EDA.
Bibliografie:ObjectType-Article-1
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ISSN:2689-1808
2689-1808
DOI:10.1109/TQE.2025.3595275