Corollary 7. There is a deterministic algorithm which, on input (bin(p),1ⁿ,1^m) with p prime and n,m≥1 , outputs a tuple in_d(_p)ⁿ detecting every nonzero polynomial computed by an acyclic scalar/variable-labelled path program with at …

Lemma 6 ([Descent by a finite coefficient ring]). Let k be a field, let n,N,E≥1 , and let V₁,…,V_{n∈_N}(k[t]_ (t) ) . Reduce their entries modulo t^E , and replace each resulting entry by its matrix of multiplication on k[t]/(t^E) in the …

Theorem 4.1 ([Order bound]). Let K be a field, let τ∈K^× have infinite multiplicative order, and let σ be the automorphism of K((z)) that fixes K and sends z to τz . Let m≥1 and ν≥0 be integers. Suppose that H∈_m(K[[z]]) satisfies σ(H)=A …

CredibilityNo verdicts yetView chain graph →

Section gives the same strictly upper triangular coefficient representation using at most m states. Thus Theorem 4.1 ([Order bound]) yields _z h_f≤n m2 for every nonzero path polynomial. With this value of N , define U_i by and apply Lemma 6 ([Descent by a finite coefficient ring]) with k=_p and E as displayed above. The same degree bound and bit analysis apply. When m=1 , every path polynomial is constant and N=E=d=1 ; the output consists of zero 1 -by- 1 matrices, which detect every nonzero constant.

Comment0

No comments yet. Found a flaw? Be the first to point it out.

Corollary 7. There is a deterministic algorithm which, on input (bin(p),1n,1m) with p prime and n,m≥1 , outputs a tuple ind(p)n detecting every nonzero polynomial computed by an acyclic scalar/variable-labelled path program with at …

Lemma 6 ([Descent by a finite coefficient ring]). Let k be a field, let n,N,E≥1 , and let V1,…,Vn∈N(k[t]_ (t) ) . Reduce their entries modulo tE , and replace each resulting entry by its matrix of multiplication on k[t]/(tE) in the …

Theorem 4.1 ([Order bound]). Let K be a field, let τ∈K× have infinite multiplicative order, and let σ be the automorphism of K((z)) that fixes K and sends z to τz . Let m≥1 and ν≥0 be integers. Suppose that H∈m(K[[z]]) satisfies σ(H)=A …

Comment0

Corollary 7. There is a deterministic algorithm which, on input (bin(p),1ⁿ,1^m) with p prime and n,m≥1 , outputs a tuple in_d(_p)ⁿ detecting every nonzero polynomial computed by an acyclic scalar/variable-labelled path program with at …

Lemma 6 ([Descent by a finite coefficient ring]). Let k be a field, let n,N,E≥1 , and let V₁,…,V_{n∈_N}(k[t]_ (t) ) . Reduce their entries modulo t^E , and replace each resulting entry by its matrix of multiplication on k[t]/(t^E) in the …

Theorem 4.1 ([Order bound]). Let K be a field, let τ∈K^× have infinite multiplicative order, and let σ be the automorphism of K((z)) that fixes K and sends z to τz . Let m≥1 and ν≥0 be integers. Suppose that H∈_m(K[[z]]) satisfies σ(H)=A …