We consider a seemingly weaker form of $\Delta^1_1$ Turing determinacy. Let $2 \leq \rho < \omega_1^{\textrm{CK}}$, $\textrm{Weak-Turing-Det}_\rho (\Delta^1_1)$ is the statement: Every set reals cofinal in degrees contains two distinct, $\Delta^0_\rho$-equivalent reals. show $\textrm{ZF}^-$: implies: for every $\nu \omega_1^{\textrm{CK}}$ there transitive model: $M \models \textrm{ZF}^- + \alep...

Non-determinacy is important in the formal specification and formal derivation of programs, but non-determinacy within expressions is theoretically problematical. The refinement calculus side-steps the problem by admitting non-determinacy only at the level of statements, leading to a style of programming that favours statements and procedures over expressions and functions. But expressions are ...

Tony Martin proved in [Mar98] that the Axiom of Determinacy AD implies the Axiom of Blackwell Determinacy Bl-AD, and conjectured that the converse holds as well: Conjecture 1 The Axiom of Blackwell Determinacy Bl-AD implies the Axiom of Determinacy AD. Although Martin, Neeman and Vervoort in their [MarNeeVer03] have made considerable progress on Martin’s Conjecture 1, the full conjecture remain...

Karp and Miller's computation graphs have been widely studied because they are a useful abstraction of multiprocessor computation. A system has the determinacy property if whenever the same set of input streams are entered into the system the resultant output is the same set of output streams. Karp and Miller showed computation graphs have this property; Woo, Smith, and Agrawala showed that dat...

This paper presents a determinacy inference analysis for logic programs. The analysis infers determinacy conditions that, if satisfied by a call, ensures that it computes at most one answer and that answer is generated only once. The principal component of the technique is a goalindependent analysis of individual clauses. This derives a condition for a call that ensures only one clause in the m...

We study the effect of subtle changes on the evolution in the scale-free (SF) networks. Three extended models are evolved based on competition and inner anti-preferential deletion in growth and preferential attachment processes. By nonlinear and dynamic controlling on randomness and determinacy, three models can self-organize into scale-free networks, and diverse scaling exponents appear. Moreo...

A skeptical worry known as ‘the indeterminacy of computation’ animates much recent philosophical reflection on the computational identity physical systems. On one hand, explanation seems to require that computing systems fall under a single, unique description at time. other, if system falls any description, it many simultaneously. Absent some principled reason take just these descriptions in p...

We announce results concerning the detailed analysis of L(R) a considerable distance along its constructibility hierarchy, assuming the axiom of determinacy. Our main focus here is on the projective hierarchy, and specifically the sizes and properties of the projective ordinals. In particular, assuming determinacy, we calculate the values of the projective ordinals, getting