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diff --git a/kaldi_io/src/tools/openfst/include/fst/expectation-weight.h b/kaldi_io/src/tools/openfst/include/fst/expectation-weight.h
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+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+//
+// Copyright 2005-2010 Google, Inc.
+// Author: krr@google.com (Kasturi Rangan Raghavan)
+// Inspiration: shumash@google.com (Masha Maria Shugrina)
+// \file
+// Expectation semiring as described by Jason Eisner:
+// See: doi=10.1.1.22.9398
+// Multiplex semiring operations and identities:
+//    One: <One, Zero>
+//    Zero: <Zero, Zero>
+//    Plus: <a1, b1> + <a2, b2> = < (a1 + a2) , (b1 + b2) >
+//    Times: <a1, b1> * <a2, b2> = < (a1 * a2) , [(a1 * b2) + (a2 * b1)] >
+//    Division: Undefined (currently)
+//
+// Usually used to store the pair <probability, random_variable> so that
+// ShortestDistance[Fst<ArcTpl<ExpectationWeight<P, V> > >]
+//    == < PosteriorProbability, Expected_Value[V] >
+
+#ifndef FST_LIB_EXPECTATION_WEIGHT_H_
+#define FST_LIB_EXPECTATION_WEIGHT_H_
+
+#include<string>
+
+#include <fst/pair-weight.h>
+
+
+namespace fst {
+
+// X1 is usually a probability weight like LogWeight
+// X2 is usually a random variable or vector
+//    see SignedLogWeight or SparsePowerWeight
+//
+// If X1 is distinct from X2, it is required that there is an external
+// product between X1 and X2 and if both semriring are commutative, or
+// left or right semirings, then result must have those properties.
+template <class X1, class X2>
+class ExpectationWeight : public PairWeight<X1, X2> {
+ public:
+  using PairWeight<X1, X2>::Value1;
+  using PairWeight<X1, X2>::Value2;
+
+  using PairWeight<X1, X2>::Reverse;
+  using PairWeight<X1, X2>::Quantize;
+  using PairWeight<X1, X2>::Member;
+
+  typedef X1 W1;
+  typedef X2 W2;
+
+  typedef ExpectationWeight<typename X1::ReverseWeight,
+                            typename X2::ReverseWeight> ReverseWeight;
+
+  ExpectationWeight() : PairWeight<X1, X2>(Zero()) { }
+
+  ExpectationWeight(const ExpectationWeight<X1, X2>& w)
+      : PairWeight<X1, X2> (w) { }
+
+  ExpectationWeight(const PairWeight<X1, X2>& w)
+      : PairWeight<X1, X2> (w) { }
+
+  ExpectationWeight(const X1& x1, const X2& x2)
+      : PairWeight<X1, X2>(x1, x2) { }
+
+  static const ExpectationWeight<X1, X2> &Zero() {
+    static const ExpectationWeight<X1, X2> zero(X1::Zero(), X2::Zero());
+    return zero;
+  }
+
+  static const ExpectationWeight<X1, X2> &One() {
+    static const ExpectationWeight<X1, X2> one(X1::One(), X2::Zero());
+    return one;
+  }
+
+  static const ExpectationWeight<X1, X2> &NoWeight() {
+    static const ExpectationWeight<X1, X2> no_weight(X1::NoWeight(),
+                                                     X2::NoWeight());
+    return no_weight;
+  }
+
+  static const string &Type() {
+    static const string type = "expectation_" + X1::Type() + "_" + X2::Type();
+    return type;
+  }
+
+  PairWeight<X1, X2> Quantize(float delta = kDelta) const {
+    return PairWeight<X1, X2>::Quantize();
+  }
+
+  ReverseWeight Reverse() const {
+    return PairWeight<X1, X2>::Reverse();
+  }
+
+  bool Member() const {
+    return PairWeight<X1, X2>::Member();
+  }
+
+  static uint64 Properties() {
+    uint64 props1 = W1::Properties();
+    uint64 props2 = W2::Properties();
+    return props1 & props2 & (kLeftSemiring | kRightSemiring |
+                              kCommutative | kIdempotent);
+  }
+};
+
+template <class X1, class X2>
+inline ExpectationWeight<X1, X2> Plus(const ExpectationWeight<X1, X2> &w,
+                                      const ExpectationWeight<X1, X2> &v) {
+  return ExpectationWeight<X1, X2>(Plus(w.Value1(), v.Value1()),
+                                   Plus(w.Value2(), v.Value2()));
+}
+
+
+template <class X1, class X2>
+inline ExpectationWeight<X1, X2> Times(const ExpectationWeight<X1, X2> &w,
+                                       const ExpectationWeight<X1, X2> &v) {
+  return ExpectationWeight<X1, X2>(Times(w.Value1(), v.Value1()),
+                                   Plus(Times(w.Value1(), v.Value2()),
+                                        Times(w.Value2(), v.Value1())));
+}
+
+template <class X1, class X2>
+inline ExpectationWeight<X1, X2> Divide(const ExpectationWeight<X1, X2> &w,
+                                        const ExpectationWeight<X1, X2> &v,
+                                        DivideType typ = DIVIDE_ANY) {
+  FSTERROR() << "ExpectationWeight::Divide: not implemented";
+  return ExpectationWeight<X1, X2>::NoWeight();
+}
+
+}  // namespace fst
+
+#endif  // FST_LIB_EXPECTATION_WEIGHT_H_