A formalization of multi-tape Turing machines

We discuss the formalization, in the Matita Theorem Prover, of basic results on multi-tapes Turing machines, up to the existence of a (certified) Universal Machine, and propose it as a natural benchmark for comparing different interactive provers and assessing the state of the art in the mechanization of formal reasoning. The work is meant to be a preliminary step towards the creation of a formal repository in Complexity Theory, and is a small piece in our long-term Reverse Complexity program, aiming to a comfortable, machine independent axiomatization of the field

Foreground automata

AbstractThis paper defines a class of on-line foreground automata, which make distinctions between the “foreground” or relevant inputs and outputs and the “blank” ones that serve as a background. It is shown that there is a well-defined operation that maps the substring of relevant inputs into an eventually appearing substring of relevant outputs, without regard for the blanks scattered among the inputs. This operation plays the role of the computation of an off-line automaton and a computational time can be measured by comparing the automaton to a “benchmark automaton” that produces each relevant output as soon as theoretically possible. Properties of these computational times are explored, both for finite automata and “Turing automata,” which are modeled by multi-tape Turing machines. An analogue of Church's Thesis can be stated for the computations associated with the operations of Turing automata, but it is argued that there is no clear cut formalization for the concept of an “effective foreground automata.

Turchin's Relation for Call-by-Name Computations: A Formal Approach

Supercompilation is a program transformation technique that was first described by V. F. Turchin in the 1970s. In supercompilation, Turchin's relation as a similarity relation on call-stack configurations is used both for call-by-value and call-by-name semantics to terminate unfolding of the program being transformed. In this paper, we give a formal grammar model of call-by-name stack behaviour. We classify the model in terms of the Chomsky hierarchy and then formally prove that Turchin's relation can terminate all computations generated by the model.Comment: In Proceedings VPT 2016, arXiv:1607.0183

Classically-Controlled Quantum Computation

Quantum computations usually take place under the control of the classical world. We introduce a Classically-controlled Quantum Turing Machine (CQTM) which is a Turing Machine (TM) with a quantum tape for acting on quantum data, and a classical transition function for a formalized classical control. In CQTM, unitary transformations and measurements are allowed. We show that any classical TM is simulated by a CQTM without loss of efficiency. The gap between classical and quantum computations, already pointed out in the framework of measurement-based quantum computation is confirmed. To appreciate the similarity of programming classical TM and CQTM, examples are given.Comment: 20 page

Model checking coalitional games in shortage resource scenarios

Verification of multi-agents systems (MAS) has been recently studied taking into account the need of expressing resource bounds. Several logics for specifying properties of MAS have been presented in quite a variety of scenarios with bounded resources. In this paper, we study a different formalism, called Priced Resource-Bounded Alternating-time Temporal Logic (PRBATL), whose main novelty consists in moving the notion of resources from a syntactic level (part of the formula) to a semantic one (part of the model). This allows us to track the evolution of the resource availability along the computations and provides us with a formalisms capable to model a number of real-world scenarios. Two relevant aspects are the notion of global availability of the resources on the market, that are shared by the agents, and the notion of price of resources, depending on their availability. In a previous work of ours, an initial step towards this new formalism was introduced, along with an EXPTIME algorithm for the model checking problem. In this paper we better analyze the features of the proposed formalism, also in comparison with previous approaches. The main technical contribution is the proof of the EXPTIME-hardness of the the model checking problem for PRBATL, based on a reduction from the acceptance problem for Linearly-Bounded Alternating Turing Machines. In particular, since the problem has multiple parameters, we show two fixed-parameter reductions.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Evolving MultiAlgebras unify all usual sequential computation models

It is well-known that Abstract State Machines (ASMs) can simulate "step-by-step" any type of machines (Turing machines, RAMs, etc.). We aim to overcome two facts: 1) simulation is not identification, 2) the ASMs simulating machines of some type do not constitute a natural class among all ASMs. We modify Gurevich's notion of ASM to that of EMA ("Evolving MultiAlgebra") by replacing the program (which is a syntactic object) by a semantic object: a functional which has to be very simply definable over the static part of the ASM. We prove that very natural classes of EMAs correspond via "literal identifications" to slight extensions of the usual machine models and also to grammar models. Though we modify these models, we keep their computation approach: only some contingencies are modified. Thus, EMAs appear as the mathematical model unifying all kinds of sequential computation paradigms.Comment: 12 pages, Symposium on Theoretical Aspects of Computer Scienc

In defense of mechanism

In Life Itself and in Essays on Life Itself, Robert Rosen (1991, 2000) argued that machines were, in principle, incapable of modeling the defining feature of living systems, which he claimed to be the existence of closed causal loops. Rosen's argument has been used to support critiques of computational models in ecological psychology. This article shows that Rosen's attack on mechanism is fundamentally misconceived. It is, in fact, of the essence of a mechanical system that it contains closed causal loops. Moreover, Rosen's epistemology is based on a strong form of indirect realism and his arguments, if correct, would call into question some of the fundamental principles of ecological psychology