Efficient state reduction methods for PLA-based sequential circuits

Experiences with heuristics for the state reduction of finite-state machines are presented and two new heuristic algorithms described in detail. Results on machines from the literature and from the MCNC benchmark set are shown. The area of the PLA implementation of the combinational component and the design time are used as figures of merit. The comparison of such parameters, when the state reduction step is included in the design process and when it is not, suggests that fast state-reduction heuristics should be implemented within FSM automatic synthesis systems

A Lower Bound of 2n2^n Conditional Branches for Boolean Satisfiability on Post Machines

We establish a lower bound of $2^n$ conditional branches for deciding the satisfiability of the conjunction of any two Boolean formulas from a set called a full representation of Boolean functions of $n$ variables - a set containing a Boolean formula to represent each Boolean function of $n$ variables. The contradiction proof first assumes that there exists a Post machine (Post's Formulation 1) that correctly decides the satisfiability of the conjunction of any two Boolean formulas from such a set by following an execution path that includes fewer than $2^n$ conditional branches. By using multiple runs of this Post machine, with one run for each Boolean function of $n$ variables, the proof derives a contradiction by showing that this Post machine is unable to correctly decide the satisfiability of the conjunction of at least one pair of Boolean formulas from a full representation of $n$-variable Boolean functions if the machine executes fewer than $2^n$ conditional branches. This lower bound of $2^n$ conditional branches holds for any full representation of Boolean functions of $n$ variables, even if a full representation consists solely of minimized Boolean formulas derived by a Boolean minimization method. We discuss why the lower bound fails to hold for satisfiability of certain restricted formulas, such as 2CNF satisfiability, XOR-SAT, and HORN-SAT. We also relate the lower bound to 3CNF satisfiability. The lower bound does not depend on sequentiality of access to the boxes in the symbol space and will hold even if a machine is capable of non-sequential access.Comment: This article draws heavily from arXiv:1406.597

A compiler approach to scalable concurrent program design

The programmer's most powerful tool for controlling complexity in program design is abstraction. We seek to use abstraction in the design of concurrent programs, so as to separate design decisions concerned with decomposition, communication, synchronization, mapping, granularity, and load balancing. This paper describes programming and compiler techniques intended to facilitate this design strategy. The programming techniques are based on a core programming notation with two important properties: the ability to separate concurrent programming concerns, and extensibility with reusable programmer-defined abstractions. The compiler techniques are based on a simple transformation system together with a set of compilation transformations and portable run-time support. The transformation system allows programmer-defined abstractions to be defined as source-to-source transformations that convert abstractions into the core notation. The same transformation system is used to apply compilation transformations that incrementally transform the core notation toward an abstract concurrent machine. This machine can be implemented on a variety of concurrent architectures using simple run-time support. The transformation, compilation, and run-time system techniques have been implemented and are incorporated in a public-domain program development toolkit. This toolkit operates on a wide variety of networked workstations, multicomputers, and shared-memory multiprocessors. It includes a program transformer, concurrent compiler, syntax checker, debugger, performance analyzer, and execution animator. A variety of substantial applications have been developed using the toolkit, in areas such as climate modeling and fluid dynamics

Completeness Results for Parameterized Space Classes

The parameterized complexity of a problem is considered "settled" once it has been shown to lie in FPT or to be complete for a class in the W-hierarchy or a similar parameterized hierarchy. Several natural parameterized problems have, however, resisted such a classification. At least in some cases, the reason is that upper and lower bounds for their parameterized space complexity have recently been obtained that rule out completeness results for parameterized time classes. In this paper, we make progress in this direction by proving that the associative generability problem and the longest common subsequence problem are complete for parameterized space classes. These classes are defined in terms of different forms of bounded nondeterminism and in terms of simultaneous time--space bounds. As a technical tool we introduce a "union operation" that translates between problems complete for classical complexity classes and for W-classes.Comment: IPEC 201