4,924 research outputs found
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Tools for reformulating logical forms into zero-one mixed integer programs (MIPS)
A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Programming (ILP) formulation or a Mixed Integer Programming (MIP) formulation is presented. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. A prototype user interface by which logical forms can be reformulated and the corresponding MIP constructed and analysed within an existing Mathematical Programming modelling system is illustrated. Finally, the steps to formulate a discrete optimisation model in this way are demonstrated by means of an example
Sublinearly space bounded iterative arrays
Iterative arrays (IAs) are a, parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this note, realtime-lAs with sublinear space bounds are used to accept formal languages. The existence of a proper hierarchy of space complexity classes between logarithmic anel linear space bounds is proved. Furthermore, an optimal spacc lower bound for non-regular language recognition is shown. Key words: Iterative arrays, cellular automata, space bounded computations, decidability questions, formal languages, theory of computatio
On two-way communication in cellular automata with a fixed number of cells
The effect of adding two-way communication to k cells one-way cellular automata (kC-OCAs) on their size of description is studied. kC-OCAs are a parallel model for the regular languages that consists of an array of k identical deterministic finite automata (DFAs), called cells, operating in parallel. Each cell gets information from its right neighbor only. In this paper, two models with different amounts of two-way communication are investigated. Both models always achieve quadratic savings when compared to DFAs. When compared to a one-way cellular model, the result is that minimum two-way communication can achieve at most quadratic savings whereas maximum two-way communication may provide savings bounded by a polynomial of degree k
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Transformation of propositional calculus statements into integer and mixed integer programs: An approach towards automatic reformulation
A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Progamming (ILP) formulation Mixed Integer Programming (MIP) formulation is presented. An ILP stated as a system of linear constraints involving integer variables and an objective function, provides a powerful representation of decision problems through a tightly interrelated closed system of choices. It supports direct representation of logical (Boolean or prepositional calculus) expressions. Binary variables (hereafter called logical variables) are first introduced and methods of logically connecting these to other variables are then presented. Simple constraints can be combined to construct logical relationships and the methods of formulating these are discussed. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. These reformulation procedures are illustrated by two examples. A scheme of implementation.ithin an LP modelling system is outlined
On one-way cellular automata with a fixed number of cells
We investigate a restricted one-way cellular automaton (OCA) model where the number of cells is bounded by a constant number k, so-called kC-OCAs. In contrast to the general model, the generative capacity of the restricted model is reduced to the set of regular languages. A kC-OCA can be algorithmically converted to a deterministic finite automaton (DFA). The blow-up in the number of states is bounded by a polynomial of degree k. We can exhibit a family of unary languages which shows that this upper bound is tight in order of magnitude. We then study upper and lower bounds for the trade-off when converting DFAs to kC-OCAs. We show that there are regular languages where the use of kC-OCAs cannot reduce the number of states when compared to DFAs. We then investigate trade-offs between kC-OCAs with different numbers of cells and finally treat the problem of minimizing a given kC-OCA
Certified Context-Free Parsing: A formalisation of Valiant's Algorithm in Agda
Valiant (1975) has developed an algorithm for recognition of context free
languages. As of today, it remains the algorithm with the best asymptotic
complexity for this purpose. In this paper, we present an algebraic
specification, implementation, and proof of correctness of a generalisation of
Valiant's algorithm. The generalisation can be used for recognition, parsing or
generic calculation of the transitive closure of upper triangular matrices. The
proof is certified by the Agda proof assistant. The certification is
representative of state-of-the-art methods for specification and proofs in
proof assistants based on type-theory. As such, this paper can be read as a
tutorial for the Agda system
SAT Modulo Linear Arithmetic for Solving Polynomial
Polynomial constraint solving plays a prominent role in several areas of
hardware and software analysis and verification, e.g., termination proving, program
invariant generation and hybrid system verification, to name a few. In this paper we
propose a new method for solving non-linear constraints based on encoding the problem
into an SMT problem considering only linear arithmetic. Unlike other existing methods,
our method focuses on proving satisfiability of the constraints rather than on proving
unsatisfiability, which is more relevant in several applications as we illustrate with
several examples. Nevertheless, we also present new techniques based on the analysis
of unsatisfiable cores that allow one to efficiently prove unsatisfiability too for a broad
class of problems. The power of our approach is demonstrated by means of extensive
experiments comparing our prototype with state-of-the-art tools on benchmarks taken
both from the academic and the industrial world
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