Abstract The efficiency and the security of smart contracts are their two fundamental properties, but might come at odds: use optimizers to enhance may introduce bugs compromise security. Our focus is on (Ethereum Virtual Machine) block-optimizations , which jump-free blocks opcodes by eliminating, reordering even changing original opcodes. We reconcile providing verification technology formall...

a4 + 1 a5 + .. . will see that a less wasteful notation, say [ a0 , a1 , a2 , . . . ] , is needed to represent it. Anyone attempting to compute the truncations [ a0 , a1 , . . . , ah ] = ph/qh will be delighted to notice that the definition [ a0 , a1 , . . . , ah ] = a0 + 1/[ a1 , . . . , ah ] immediately implies by induction on h that there is a correspondence ( a0 1 1 0 ) ( a1 1 1 0 ) · · · (...

In this note, we will consider the question of local equivalence of analytic functions which fix the origin and are tangent to the identity, as well as the question of flows of analytic vector fields. All mappings and equivalences are considered in the non-archimedean context e.g. all norms can be considered p-adic norms. We show that any two mappings f and g which are formally equivalent are a...

involving additional fields Φ̂I(z1)Φ̂I(z2) · · ·. Note that in eq. (3) the fields are in the interaction rather than Heisenberg picture, so they evolve with time as free fields according to the free Hamiltonian Ĥ0. Likewise, |0〉 is the free theory’s vacuum, i.e. the ground state of the free Hamiltonian Ĥ0 rather than the full Hamiltonian Ĥ. To work out the relation between (1) and (3), we start b...

The effective action induced by chiral fermions can be written, formally, as an overlap of two states. These states are the Fock ground states of Hamiltonians for fermions in even dimensional space with opposite sign mass terms coupled to identical static vector potentials. A perturbative analysis of the overlap in the continuum framework produces the correct anomaly for Abelian gauge fields in...