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We present a systematic approach for solving graph problems under the network models. We illustrate this approach on the mesh-of-trees networks. It is known that under the CREW PRAM model, when a undirected graph of n nodes is given by an n by n adjacency matrix, the problems of finding minimum spanning forest, connected components, and biconnected components can all be solved with optimal speedup...
We present a method of reasoning directly about functional programs in Second-Order Logic, based on the use of explicit second-order definitions for inductively defined data-types. Termination becomes a special case of correct typing. The formula-as-type analogy known from Proof Theory, when applied to this formalism, yields λ-expressions representing objects of inductively defined types, as well...
We define a process logic PL that subsumes Pratt's process logic, Parikh's SOAPL, Nishimura's process logic, and Pnueli's Temporal Logic in expressiveness. The language of PL is an extension of the language of Propositional Dynamic Logic (PDL). We give a deductive system for PL which includes the Segerberg axioms for PDL and prove that it is complete. We also show that PL is decidable.
Problems concerned with finding inscribing or circumscribing polygons that maximize some measurement are considered such as: Find an area maximizing triangle inscribed in a given convex polygon. Algorithms solving a number of these problems in linear time are presented. They use the common approach of finding an initial solution with respect to a fixed bounding point and then iteratively transforming...
This paper gives a personal account of some developments in automata theory and computational complexity theory. Though the account is subjective and deals primarily with the research areas of direct interest to the author, it discusses the underlying beliefs and philosophy which guided this research as well as the intellectual environment and the ideas and contacts which influenced it. An attempt...
Upper and lower bounds are proved for the shared space requirements for solution of several problems involving resource allocation among asynchronous processes. Controlling the degradation of performance when a limited number of processes fail is of particular interest.
A model of parallel computation based on a generalization of nondeterminism in Turing machines is introduced. Complexity classes //T(n)-TIME, //L(n)-SPACE, //LOGSPACE, //PTIME, etc. are defined for these machines in a way analogous to T(n)-TIME, L(n)-SPACE, LOGSPACE, PTIME, etc. for deterministic machines. It is shown that, given appropriate honesty conditions, L(n)-SPACE ⊆ //L(n)2-TIME T(n)-TIME...
Straight line programs in which array elements can be referenced and set are considered. Two programs are equivalent if they compute the same expression as a function of the inputs. Testing the equivalence of programs with arrays is shown to be NP-complete, while programs without arrays can be tested for equivalence in linear time. Equivalence testing takes polynomial time when programs have either...
In this note we show that the tape bounded complexity classes of languages over single letter alphabets are closed under complementation. We then use this result to show that there exists an infinite hierarchy of tape bounded complexity classes of sla languages between log n and log log n tape bounds. We also show that every infinite sla language recognizable on less than log n tape has infinitely...
In this paper Valiant's decision procedure for equivalence of deterministic finite-turn pushdown machines is improved upon. The improved equivalence test is: Given two mahcines, one constructs a pushdown machine that simulates them simultaneously and accepts a string iff it is accepted by exactly one of them. The given machines are equivalent iff the simulating pda accepts the empty language. The...
Decision procedures for validity in intuitionistic propositional calculus and modal propositional calculus are given which require a running time proportional to a polynomial in the length of the formula on a nondeterministic Turing machine. Using a theorem of Cook's and well-known transformations from intuitionistic to classical and modal to intuitionistic logics, the validity problem for intuitionistic...
The purpose of this paper is to gain a better understanding of the structure of undecidable problems in automata theory by investigating the degree of unsolvability of these problems. This is achieved by using Turing machines with oracles to define when one undecidable problem can be reduced to another and to establish an infinite hierarchy of (equivalent) undecidable problems. This hierarchy is then...
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