A SAT+CAS Approach to Finding Good Matrices: New Examples and Counterexamples

We enumerate all circulant good matrices with odd orders divisible by 3 up to order 70. As a consequence of this we find a previously overlooked set of good matrices of order 27 and a new set of good matrices of order 57. We also find that circulant good matrices do not exist in the orders 51, 63, and 69, thereby finding three new counterexamples to the conjecture that such matrices exist in all odd orders. Additionally, we prove a new relationship between the entries of good matrices and exploit this relationship in our enumeration algorithm. Our method applies the SAT+CAS paradigm of combining computer algebra functionality with modern SAT solvers to efficiently search large spaces which are specified by both algebraic and logical constraints

(Un)Decidability Results for Word Equations with Length and Regular Expression Constraints

We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality over string terms (word equations), linear inequality over the length function (length constraints), and membership in regular sets. These questions are important in logic, program analysis, and formal verification. Variants of these questions have been studied for many decades by mathematicians. More recently, practical satisfiability procedures (aka SMT solvers) for these formulas have become increasingly important in the context of security analysis for string-manipulating programs such as web applications. We prove three main theorems. First, we give a new proof of undecidability for the validity problem for the set of sentences written as a forall-exists quantifier alternation applied to positive word equations. A corollary of this undecidability result is that this set is undecidable even with sentences with at most two occurrences of a string variable. Second, we consider Boolean combinations of quantifier-free formulas constructed out of word equations and length constraints. We show that if word equations can be converted to a solved form, a form relevant in practice, then the satisfiability problem for Boolean combinations of word equations and length constraints is decidable. Third, we show that the satisfiability problem for quantifier-free formulas over word equations in regular solved form, length constraints, and the membership predicate over regular expressions is also decidable.Comment: Invited Paper at ADDCT Workshop 2013 (co-located with CADE 2013

A Prototype Design of Bibliographic Database for Doctoral Theses Using WINISIS : a practical approach

This article explores the techniques for designing and managing the bibliographical database by using the Windows-based ISIS (WINISIS) library software package and specified the brief description of steps taken to create a database of all bibliographic materials as well as features of WINSIS are taken into consideration. The purpose of the paper is to be acquainted college librarians with the distinctive features of the Windows-based ISIS because Microsoft Windows is described as a graphical user environment, which gives the user more control over the work as well as enables the user to use more of the power of the computer. The author has applied practical methods to put forth the techniques for designing and managing the bibliographical database of Doctoral Theses by using WINISIS software package. The author has attempted to find out various aspects to describe the features of the various modules of Windows-based ISIS (WINSIS) library software which would be valuable for those college librarians who faced the crunch of budget and are distressed to manage databases, especially those colleges are situated in rural and tribal areas of India. This paper is originally based on the dissertation made by the author in Degree of Master of Philosophy which is recognized and essential in the research purview of higher education