Scalar Ambiguity and Freeness in Matrix Semigroups over Bounded Languages

Bell, Paul C.; Chen, Shang; Jackson, Lisa M.

doi:10.1007/978-3-319-30000-9_38

Cited by 6 publications

(6 citation statements)

References 14 publications

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“…We can now state Theorem 3 is undecidable over integer matrices, with an increase in the dimension (note that this increased dimension was erroneously omitted in [21]). Proof.…”

Section: Scalar Ambiguity and Freeness For Matricesmentioning

confidence: 97%

Freeness properties of weighted and probabilistic automata over bounded languages

Bell

Chen

Jackson

2019

Information and Computation

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“…We can now state Theorem 3 is undecidable over integer matrices, with an increase in the dimension (note that this increased dimension was erroneously omitted in [21]). Proof.…”

Section: Scalar Ambiguity and Freeness For Matricesmentioning

confidence: 97%

Freeness properties of weighted and probabilistic automata over bounded languages

Bell

Chen

Jackson

2019

Information and Computation

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“…, x t ). For each term T j , we define a set of t + 1 integer matrices, corresponding to a t + 1-letter weighted finite automaton 4 defined by (u j , {X j, |0 ≤ ≤ t}, v j ) such that (u j ) T X x0 j,0 X x1 j,1 • • • X xt j,t v j = T j (x 0 , x 1 , . .…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…This problem is known to be undecidable [29], even for a fixed number of dimensions and for two input matrices [8,21]. A second natural question is the freeness problem (or injectivity problem) for PFA, studied in [4] -given a PFA P over alphabet Σ determine whether the acceptance function f P (w) is injective (i.e. do there exist two distinct words with the same acceptance probability).…”

Section: Introductionmentioning

confidence: 99%

Polynomially Ambiguous Probabilistic Automata on Restricted Languages

Bell¹

2019

Preprint

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We consider the computability and complexity of decision questions for Probabilistic Finite Automata (PFA) with sub-exponential ambiguity. We show that the emptiness problem for strict and non-strict cut-points of polynomially ambiguous commutative PFA remains undecidable, implying that the problem is undecidable when inputs are from a letter monotonic language. We show that the problem remains undecidable over a binary input alphabet when the input word is over a bounded language, in the noncommutative case. In doing so, we introduce a new technique based upon the Turakainen construction of a PFA from a Weighted Finite Automata which can be used to generate PFA of lower dimensions and of subexponential ambiguity. We also study freeness/injectivity problems for polynomially ambiguous PFA and study the border of decidability and tractability for various cases.

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“…A second natural question is the freeness problem (or injectivity problem) for PFA, studied in [3] -given a PFA P over alphabet Σ determine whether the acceptance function f P (w) is injective (i.e. do there exist two distinct words with the same acceptance probability).…”

Section: Introductionmentioning

confidence: 99%