Guessing Individual Sequences: Generating Randomized Guesses Using Finite-State Machines
Motivated by earlier results on universal randomized guessing, we consider an individual-sequence approach to the guessing problem: in this setting, the goal is to guess a secret, individual (deterministic) vector <inline-formula> <tex-math notation="LaTeX">x^{n}=(x_{1},\ldots,...
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| Vydáno v: | IEEE transactions on information theory Ročník 66; číslo 5; s. 2912 - 2920 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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IEEE
01.05.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | Motivated by earlier results on universal randomized guessing, we consider an individual-sequence approach to the guessing problem: in this setting, the goal is to guess a secret, individual (deterministic) vector <inline-formula> <tex-math notation="LaTeX">x^{n}=(x_{1},\ldots,x_{n}) </tex-math></inline-formula>, by using a finite-state machine that sequentially generates randomized guesses from a stream of purely random bits. We define the finite-state guessing exponent as the asymptotic normalized logarithm of the minimum achievable moment of the number of randomized guesses, generated by any finite-state machine, until <inline-formula> <tex-math notation="LaTeX">x^{n} </tex-math></inline-formula> is guessed successfully. We show that the finite-state guessing exponent of any sequence is intimately related to its finite-state compressibility (due to Lempel and Ziv), and it is asymptotically achieved by the decoder of (a certain modified version of) the 1978 Lempel-Ziv data compression algorithm (a.k.a. the LZ78 algorithm), fed by purely random bits. The results are also extended to the case where the guessing machine has access to a side information sequence, <inline-formula> <tex-math notation="LaTeX">y^{n}=(y_{1},\ldots,y_{n}) </tex-math></inline-formula>, which is also an individual sequence. |
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| AbstractList | Motivated by earlier results on universal randomized guessing, we consider an individual–sequence approach to the guessing problem: in this setting, the goal is to guess a secret, individual (deterministic) vector [Formula Omitted], by using a finite–state machine that sequentially generates randomized guesses from a stream of purely random bits. We define the finite–state guessing exponent as the asymptotic normalized logarithm of the minimum achievable moment of the number of randomized guesses, generated by any finite–state machine, until [Formula Omitted] is guessed successfully. We show that the finite–state guessing exponent of any sequence is intimately related to its finite–state compressibility (due to Lempel and Ziv), and it is asymptotically achieved by the decoder of (a certain modified version of) the 1978 Lempel–Ziv data compression algorithm (a.k.a. the LZ78 algorithm), fed by purely random bits. The results are also extended to the case where the guessing machine has access to a side information sequence, [Formula Omitted], which is also an individual sequence. Motivated by earlier results on universal randomized guessing, we consider an individual-sequence approach to the guessing problem: in this setting, the goal is to guess a secret, individual (deterministic) vector <inline-formula> <tex-math notation="LaTeX">x^{n}=(x_{1},\ldots,x_{n}) </tex-math></inline-formula>, by using a finite-state machine that sequentially generates randomized guesses from a stream of purely random bits. We define the finite-state guessing exponent as the asymptotic normalized logarithm of the minimum achievable moment of the number of randomized guesses, generated by any finite-state machine, until <inline-formula> <tex-math notation="LaTeX">x^{n} </tex-math></inline-formula> is guessed successfully. We show that the finite-state guessing exponent of any sequence is intimately related to its finite-state compressibility (due to Lempel and Ziv), and it is asymptotically achieved by the decoder of (a certain modified version of) the 1978 Lempel-Ziv data compression algorithm (a.k.a. the LZ78 algorithm), fed by purely random bits. The results are also extended to the case where the guessing machine has access to a side information sequence, <inline-formula> <tex-math notation="LaTeX">y^{n}=(y_{1},\ldots,y_{n}) </tex-math></inline-formula>, which is also an individual sequence. |
| Author | Merhav, Neri |
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| Snippet | Motivated by earlier results on universal randomized guessing, we consider an individual-sequence approach to the guessing problem: in this setting, the goal... Motivated by earlier results on universal randomized guessing, we consider an individual–sequence approach to the guessing problem: in this setting, the goal... |
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| SubjectTerms | Algorithms Asymptotic properties Binary trees Compressibility Data compression Decoding finite–state machine Guessing exponent Hidden Markov models incremental parsing individual sequences Lempel–Ziv algorithm Password Probabilistic logic Randomization randomized guessing sequence complexity side information State machines Viterbi algorithm |
| Title | Guessing Individual Sequences: Generating Randomized Guesses Using Finite-State Machines |
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