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diff --git a/kaldi_io/src/tools/openfst/include/fst/power-weight.h b/kaldi_io/src/tools/openfst/include/fst/power-weight.h
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+// power-weight.h
+
+// 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: allauzen@google.com (Cyril Allauzen)
+//
+// \file
+// Cartesian power weight semiring operation definitions.
+
+#ifndef FST_LIB_POWER_WEIGHT_H__
+#define FST_LIB_POWER_WEIGHT_H__
+
+#include <fst/tuple-weight.h>
+#include <fst/weight.h>
+
+
+namespace fst {
+
+// Cartesian power semiring: W ^ n
+// Forms:
+//  - a left semimodule when W is a left semiring,
+//  - a right semimodule when W is a right semiring,
+//  - a bisemimodule when W is a semiring,
+//    the free semimodule of rank n over W
+// The Times operation is overloaded to provide the
+// left and right scalar products.
+template <class W, unsigned int n>
+class PowerWeight : public TupleWeight<W, n> {
+ public:
+  using TupleWeight<W, n>::Zero;
+  using TupleWeight<W, n>::One;
+  using TupleWeight<W, n>::NoWeight;
+  using TupleWeight<W, n>::Quantize;
+  using TupleWeight<W, n>::Reverse;
+
+  typedef PowerWeight<typename W::ReverseWeight, n> ReverseWeight;
+
+  PowerWeight() {}
+
+  PowerWeight(const TupleWeight<W, n> &w) : TupleWeight<W, n>(w) {}
+
+  template <class Iterator>
+  PowerWeight(Iterator begin, Iterator end) : TupleWeight<W, n>(begin, end) {}
+
+  static const PowerWeight<W, n> &Zero() {
+    static const PowerWeight<W, n> zero(TupleWeight<W, n>::Zero());
+    return zero;
+  }
+
+  static const PowerWeight<W, n> &One() {
+    static const PowerWeight<W, n> one(TupleWeight<W, n>::One());
+    return one;
+  }
+
+  static const PowerWeight<W, n> &NoWeight() {
+    static const PowerWeight<W, n> no_weight(TupleWeight<W, n>::NoWeight());
+    return no_weight;
+  }
+
+  static const string &Type() {
+    static string type;
+    if (type.empty()) {
+      string power;
+      Int64ToStr(n, &power);
+      type = W::Type() + "_^" + power;
+    }
+    return type;
+  }
+
+  static uint64 Properties() {
+    uint64 props = W::Properties();
+    return props & (kLeftSemiring | kRightSemiring |
+                    kCommutative | kIdempotent);
+  }
+
+  PowerWeight<W, n> Quantize(float delta = kDelta) const {
+    return TupleWeight<W, n>::Quantize(delta);
+  }
+
+  ReverseWeight Reverse() const {
+    return TupleWeight<W, n>::Reverse();
+  }
+};
+
+
+// Semiring plus operation
+template <class W, unsigned int n>
+inline PowerWeight<W, n> Plus(const PowerWeight<W, n> &w1,
+                              const PowerWeight<W, n> &w2) {
+  PowerWeight<W, n> w;
+  for (size_t i = 0; i < n; ++i)
+    w.SetValue(i, Plus(w1.Value(i), w2.Value(i)));
+  return w;
+}
+
+// Semiring times operation
+template <class W, unsigned int n>
+inline PowerWeight<W, n> Times(const PowerWeight<W, n> &w1,
+                               const PowerWeight<W, n> &w2) {
+  PowerWeight<W, n> w;
+  for (size_t i = 0; i < n; ++i)
+    w.SetValue(i, Times(w1.Value(i), w2.Value(i)));
+  return w;
+}
+
+// Semiring divide operation
+template <class W, unsigned int n>
+inline PowerWeight<W, n> Divide(const PowerWeight<W, n> &w1,
+                                const PowerWeight<W, n> &w2,
+                                DivideType type = DIVIDE_ANY) {
+  PowerWeight<W, n> w;
+  for (size_t i = 0; i < n; ++i)
+    w.SetValue(i, Divide(w1.Value(i), w2.Value(i), type));
+  return w;
+}
+
+// Semimodule left scalar product
+template <class W, unsigned int n>
+inline PowerWeight<W, n> Times(const W &s, const PowerWeight<W, n> &w) {
+  PowerWeight<W, n> sw;
+  for (size_t i = 0; i < n; ++i)
+    sw.SetValue(i, Times(s, w.Value(i)));
+  return w;
+}
+
+// Semimodule right scalar product
+template <class W, unsigned int n>
+inline PowerWeight<W, n> Times(const PowerWeight<W, n> &w, const W &s) {
+  PowerWeight<W, n> ws;
+  for (size_t i = 0; i < n; ++i)
+    ws.SetValue(i, Times(w.Value(i), s));
+  return w;
+}
+
+// Semimodule dot product
+template <class W, unsigned int n>
+inline W DotProduct(const PowerWeight<W, n> &w1,
+                    const PowerWeight<W, n> &w2) {
+  W w = W::Zero();
+  for (size_t i = 0; i < n; ++i)
+    w = Plus(w, Times(w1.Value(i), w2.Value(i)));
+  return w;
+}
+
+
+}  // namespace fst
+
+#endif  // FST_LIB_POWER_WEIGHT_H__