200,761 research outputs found
Propositional logic with short-circuit evaluation: a non-commutative and a commutative variant
Short-circuit evaluation denotes the semantics of propositional connectives
in which the second argument is evaluated only if the first argument does not
suffice to determine the value of the expression. Short-circuit evaluation is
widely used in programming, with sequential conjunction and disjunction as
primitive connectives.
We study the question which logical laws axiomatize short-circuit evaluation
under the following assumptions: compound statements are evaluated from left to
right, each atom (propositional variable) evaluates to either true or false,
and atomic evaluations can cause a side effect. The answer to this question
depends on the kind of atomic side effects that can occur and leads to
different "short-circuit logics". The basic case is FSCL (free short-circuit
logic), which characterizes the setting in which each atomic evaluation can
cause a side effect. We recall some main results and then relate FSCL to MSCL
(memorizing short-circuit logic), where in the evaluation of a compound
statement, the first evaluation result of each atom is memorized. MSCL can be
seen as a sequential variant of propositional logic: atomic evaluations cannot
cause a side effect and the sequential connectives are not commutative. Then we
relate MSCL to SSCL (static short-circuit logic), the variant of propositional
logic that prescribes short-circuit evaluation with commutative sequential
connectives.
We present evaluation trees as an intuitive semantics for short-circuit
evaluation, and simple equational axiomatizations for the short-circuit logics
mentioned that use negation and the sequential connectives only.Comment: 34 pages, 6 tables. Considerable parts of the text below stem from
arXiv:1206.1936, arXiv:1010.3674, and arXiv:1707.05718. Together with
arXiv:1707.05718, this paper subsumes most of arXiv:1010.367
Short circuit protection for a power distribution system
Sensing circuit detects when the output from a matrix is present and when it should be present. The circuit provides short circuit protection for a power distribution system where the selection of the driven load is accomplished by digital logic
An independent axiomatisation for free short-circuit logic
Short-circuit evaluation denotes the semantics of propositional connectives
in which the second argument is evaluated only if the first argument does not
suffice to determine the value of the expression. Free short-circuit logic is
the equational logic in which compound statements are evaluated from left to
right, while atomic evaluations are not memorised throughout the evaluation,
i.e., evaluations of distinct occurrences of an atom in a compound statement
may yield different truth values. We provide a simple semantics for free SCL
and an independent axiomatisation. Finally, we discuss evaluation strategies,
some other SCLs, and side effects.Comment: 36 pages, 4 tables. Differences with v2: Section 2.1: theorem
Thm.2.1.5 and further are renumbered; corrections: p.23, line -7, p.24, lines
3 and 7. arXiv admin note: substantial text overlap with arXiv:1010.367
Generalized disjunction decomposition for evolvable hardware
Evolvable hardware (EHW) refers to self-reconfiguration hardware design, where the configuration is under the control of an evolutionary algorithm (EA). One of the main difficulties in using EHW to solve real-world problems is scalability, which limits the size of the circuit that may be evolved. This paper outlines a new type of decomposition strategy for EHW, the “generalized disjunction decomposition” (GDD), which allows the evolution of large circuits. The proposed method has been extensively tested, not only with multipliers and parity bit problems traditionally used in the EHW community, but also with logic circuits taken from the Microelectronics Center of North Carolina (MCNC) benchmark library and randomly generated circuits. In order to achieve statistically relevant results, each analyzed logic circuit has been evolved 100 times, and the average of these results is presented and compared with other EHW techniques. This approach is necessary because of the probabilistic nature of EA; the same logic circuit may not be solved in the same way if tested several times. The proposed method has been examined in an extrinsic EHW system using theevolution strategy. The results obtained demonstrate that GDD significantly improves the evolution of logic circuits in terms of the number of generations, reduces computational time as it is able to reduce the required time for a single iteration of the EA, and enables the evolution of larger circuits never before evolved. In addition to the proposed method, a short overview of EHW systems together with the most recent applications in electrical circuit design is provided
Non-commutative propositional logic with short-circuited biconditional and NAND
Short-circuit evaluation denotes the semantics of propositional connectives
in which the second argument is evaluated only if the first argument does not
suffice to determine the value of the expression. In programming, short-circuit
evaluation is widely used, with left-sequential conjunction and disjunction as
primitive connectives. We consider left-sequential, non-commutative
propositional logic, also known as MSCL (memorising short-circuit logic), and
start from a previously published, equational axiomatisation. First, we extend
this logic with a left-sequential version of the biconditional connective,
which allows for an elegant axiomatisation of MSCL. Next, we consider a
left-sequential version of the NAND operator (the Sheffer stroke) and again
give a complete, equational axiomatisation of the corresponding variant of
MSCL. Finally, we consider these logical systems in a three-valued setting with
a constant for `undefined', and again provide completeness results.Comment: 21 pages, 6 table
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